The iPhone 5C already has a backdoor; that's the problem. Furthermore, you can be certain that the NSA and other agencies can get in through that back door. Apple winning or losing makes no difference to that. But if Apple wins, it gives the appearance that your data is protected when in fact it is not. Furthermore, if Apple wins, it will give more ammunition to people demanding laws that require explicit backdoors.
So in your opinion we are damned if we do and damned if we don't? The lack of completely secure phones today (or at least back when the iPhone 5C was sold) completely invalidates any potential advances to make them more secure in the future, and if Apple wins in court then the legislature will (despite having failed to do so during the first encryption debate) of course pass laws to grant such a back door in the future. That's an awfully pessimistic view. If legislators from my state start supporting such a bill, they will get an earful from me, and I imagine that most of the tech industry will throw their lobbying weight around as well to prevent such a bill.
We know such a phone would be affordable, easy to use, and popular: there would be no user visible changes. Nor would it be any more expensive, because Apple already has a custom, secure crypto chip that could have implemented the PIN wipe securely without backdoors and at no extra cost.
You may believe that, but I see no reason to believe you are correct. There is a cost, even if not in money, to a completely secure phone. The costs are time and the hassle of remembering, or sharing it when you ask someone else to use your phone for you, etc. Those may be small costs, but to some they are big enough to result in many people still not having even a 4 character pin to protect their phone. You and I may value security (probably to differing degrees), but many don't at all, and requiring a pin that could wipe the phone if a kid gets their hands on it and tries too many wrong passwords/pins scares many. Myself included. I've been locked out of my phone several times because my 2 year old got the phone and tried to get into it, or because it became activated in my pocket some how and ran up several attempts without any deliberate action on my part.
Security may be easy in a technical sense, but to make something that is both secure, easy to use, and desirable to a wide range of buyers all at the same time is something different entirely. Apple prioritized ease of use and desirability over security. Their call, don't buy if you don't want, but they've increased their emphasis on security over time. Maybe they'll never get to where you'd like them to be, but I'm glad for any improvement since I hate the Android and Windows phones I've used thus far. A little protection is better than none.
My guess is that the weak security architecture of the iPhone 5C was deliberate
And unless you've got real evidence, that is just an opinion. And not even one that is logically consistent, since one of the issues at the heart of this case is that the iPhone 6 and 6S are even more secure, meaning the work around that the FBI wants Apple to implement for the 5C won't work on these newer phones.
Cook should build phones that just cannot be broken into, not even by someone with full access to the source code, firmware signing keys, and hardware.
That does appear to be the way he is pushing his engineers. However, in the mean time there are billions of iPhones out there for whom this level of protection is not yet possible, and cannot be retroactively applied. I don't even believe that Cook has attempted to portray his actions as altruistic, just that what is in the best interest of Apple Inc., and what is in the best interest of owners of Apple devises are in sync with each other on this issue.
Apple Inc sees no value and only cost associated with developing and maintaining a special version of IOS that can be used to by-pass their current security protocols. If Apple had already developed such a device on their own he wouldn't be able to keep the FBI from requesting that he use it on their behalf. However, the tools don't exist precisely because Apple sees no value in creating them other than avoiding a very public fight with the FBI over this issue. The negative PR from this is nothing compared to the negative PR of those tools escaping and getting into the hands of identify thieves, or celebrity stalkers, or hostile foreign governments, etc.
Keep in mind that Cook is a gay man, and he managed to keep that more or less a secret for most of his career as a public figure at Apple. In 2016 that doesn't mean what it used to in the US, but in Russia and many other countries around the world it is a crime that can lead to incarceration, torture, and death. I wouldn't be surprised if for Mr. Cook personally, the idea that a government that would view people like him as sub-human or criminals due to their sexual preference might request the exact same tools that the FBI is requesting is terrifying. Or if you want to take sexual preference off of the table, you can trot out any persecuted minority. China very recently planned on passing a law of similar scope and due to pressure from the US government and western technology companies they abandoned it. If the US creates this precedent, the Chinese will take it even further, and while you may think the FBI is trustworthy I doubt most people would extend similar trust to the governments of every country in which Apple operates.
Stinginess with privileges is kindness in disguise. -- Guide to VAX/VMS Security, Sep. 1984