First, with regards to the rental house thing, that's a complete non-sequitur. You have the same right against unreasonable search there you do at your own home, in a hotel room, or any place you stay overnight. For the purpose of the fourth amendment protection against unreasonable search of your home, anywhere you're sleeping that night becomes "home."
"Without your participation it wouldn't come into existence" also doesn't work, because that would preclude any evidence of anything you've ever done, ever.
I think there's several points of confusion here, having to do with 1) the reasonableness of the 3rd party doctrine and 2) a confusion over the different nature, not just standard of evidence, of a subpoena and a warrant.
First, understand "privacy" is not and cannot ever be an absolute right in a functioning society. You are the armed robber who put a gun in my face and swore you'd kill me if I didn't hand over the $47 in my boss's cash drawer and now I can't sleep and don't feel safe anywhere I go. I want you behind bars, and society wants you behind bars so you can't do that to anyone else, but due process of law demands evidence to convict you. That evidence must be collected. Which means, privacy (yours and perhaps others) must be invaded in order for justice to be served. But, we want to guard against abuse of the power to invade your privacy, so we have safeguards against unreasonable search and seizure. The goal of which is to minimize and hopefully eliminate invasions of privacy. The less invasive of your privacy the collection of the evidence is, the lower the standard of evidence needed for the collection.
There is a much, much lower standard of evidence required for a subpoena than a warrant, and with good reason. A subpoena is an order to YOU to comply with the court. You are ordered to produce specific materials, or present yourself or your testimony, to the court. You are ordered to do so by an officer of the court. Different states have different procedures of course, but in general, you can be subpoenaed by a judge, by a clerk of the court, by a lawyer (defense or prosecution). If you're defending yourself you can get blank subpoenas from the clerk of the court. You can compel the ice cream shop across town to produce the video footage of you buying ice cream at the time of the robbery, exonerating you, even though the shop owner doesn't want to because he hates whatever color your skin is. But in the interests of justice, no, the court (and society) demands he do it anyway.
But the nice thing about subpoenas is you can contest them before producing anything. You can stop harm to your privacy from being done at all! You can say "what you're asking for doesn't exist" and provide reasonable explanations. You can say "what you're asking for is irrelevant to the matter before the court." You can say "no, I won't produce this because it is too invasive of my privacy."
That last part's kind of important. Because the subject of the subpoena (in 3rd party cases like this one) is the one whose information is being seized, not the person suspected of the crime. Let's say you buy a pencil from me, and I issue you a receipt. That receipt is your transaction record. I also keep a ledger wherein I record that you purchased a pencil from me. That is my transaction record. Do you have any rights to my record? No. I can post it on the internet. k4tt bought a pencil here. There's nothing you can do about it. It's my record. And you can do the same. "I bought a pencil from meta-monkey and here's the proof!" and I have no authority to stop you from doing so with your record of our transaction.
When you stab somebody in the face with that pencil and the court asks me if I have a record of the purchase of that pencil, I have absolutely no obligation to you to not turn over my receipt of the sale. None. It's my record. But, turning it over is an invasion of MY privacy, not yours. You never had any privacy rights to my record of our transaction at all. Now, first, I would gladly hand over the record, because what the fuck you're stabbing people in the face with pencils. And if I said no, it's reasonable for society to compel me to turn over that one record. It's a very minor invasion of my privacy in the interests of justice. Now if they wanted ALL my records, of people for whom no evidence of pencil-stabbing exists, that's a different story. And if they did that, I'd contest that part of the subpoena as irrelevant to the matter before the court (whether or not YOU stabbed somebody with a pencil) and far too invasive.
So that's kind of nice. The court asks me nicely (but firmly) for a specific thing of mine, that's relevant to a specific matter before the court, allows me time to produce it in a manner that minimizes any invasion of my privacy and doesn't disclose the pencil-purchasing habits of my other customers.
Now let's talk about warrants. Yes, there's a higher standard of evidence required for the issuance of a warrant. And that's because while a subpoena compels ME to cooperate with the officers of the court, a warrant ORDERS officers of the law to DO whatever the warrant says, fuck anything I do or say. It orders them to do things that would otherwise be illegal (force their way onto my property, subdue me, go through my shit) and grants them immunity from punishment for the otherwise illegal actions. When a warrant is issued to search my pencil store for the record of your purchase, fuck me. It's not like "asking but WE REALLY MEAN IT THIS TIME." There is no "compliance." They might knock on the door, but it doesn't matter if I "let them in" or not. They're coming in, they will remove me from the premises while they conduct their search, they will go through my receipt drawer, they will look at all my receipts and those of all my other customers until they find the one (the one of your purchase) that they're looking for. In the meantime, they see all my shit, and lots of stuff about all my other customers. And that's not a new "oh no police state!" thing. That's how warrants have always worked.
What's required for the SCA, though, is a court order signed by a judge who's been presented with articulable facts about the commission of a specific crime by a specific person and he finds reasonable cause. So a warrant is a court order signed by a judge, but so is a subpoena signed by a judge. And that's specifically to address the fact that people don't want phone records being casually perused. And, there are criminal penalties for supplying such records to any government entity without the signed order. So phone records are already protected more than other records, like the pencil receipt.
By your line of thought, its reasonble for law enforccement to search any and all objects which you have not sole ownership over. Think creditcards, library cards, banking accounts, utility bills, facebook activity, rental cars, rental homes.
Without a search warrant?
Of course they should have to have a search warrant in order to search those things! My god man! It is completely ridiculous to think police could just barge into FaceBook data centers or the library and start rifling through stuff without a search warrant! On what planet? No, there is nothing I've said that in any way indicates that's okay. How on earth do you get that?
No, if they want those things by force they need a warrant. If they want them produced for them, they need subpoenas, to compel the record owners to comply with a reasonable court order, which they can challenge. And in the case of communication records (like FaceBook, or email), they need an order signed by a judge. And in all cases it needs to be relevant to a matter before the court. There is no blanket surveillance or fishing expeditions going on here. Just regular due process of law.
Which is what I want the fucking NSA to do. You think I'm a terrorist? Fine. Convince a judge there's reasonable cause to search just my shit for commission of a specific crime. But to just go collecting everything, all the time, from everybody is monstrously insane.
Back to this case, I absolutely, absolutely do not want courts issuing warrants when a subpoena will do, and I don't know why you do. A warrant is completely excessive when being asked to hand over a specific piece of evidence relevant to a specific crime committed by a specific third party. Is that what you want? No subpoenas? Only warrants? The government should have forced their way into the phone company, seized their records and searched through EVERYBODY'S stuff until they found the records for the suspect here?
Isn't it far more reasonable to issue a subpoena for just the specific information relevant to the case, after it had been demonstrated to a judge that it would be reasonable to do so? And the phone company is then able to sanitize the data, to expose only the bits that are reasonable and relevant to the specific matter before the court?
There's definitely enough evidence in this case to meet the standards of evidence for a warrant.
Option A: Subpoena signed by a judge. "You are ordered to produce these specific items unless you can tell us a good reason why not."
Option B: Warrant. "Fuck your shit, we are taking your stuff and searching it until we find these specific things."
Why do you prefer B?