I doubt there's a company in the land that would recruit an unknown, straight off the street, give them a salaried post and let them work 100% from home.
This is false. A very good friend of mine works exclusively out of his house as a developer. Many of the developers at his company are work-from home types and have always been work-from home employees.
Additionally, there are software jobs that are true work from home positions and are advertised as such. I've had recruiters start to approach me about such jobs.
Finally, I've had a 15 year career at Microsoft. In the last 6 months, I've been given the flexibility to WFH as much as I like to. I'm currently at home for the summer.
When I asked earlier in my career, the answer was no. I'm slightly more valuable than I was then, but, the nature of my team and my work has changed such that a WFH role is more plausible than it once was.
I know a handful of other Microsoft employees who are full time WFH and who have no Microsoft office anywhere. I still have an office and I use it about 50% during the school year.
As far as how you get this arrangement
1) if you're a high value contributor with the right kind of manager on the right kind of team, even in an organization that doesn't really do remote work, you can basically play the card that says, "I am moving. I would like to keep working here, for you, and I understand what that will do to my long term career velocity here, but, whether you keep me or not, I am moving"
Sometimes that works, sometimes it doesn't. If you get a new team or a new manager, you can be let go. "The deal can be altered", so to speak. Of course, the deal can (and is) altered anyway, even for office people. So, it's a matter of priorities and risk tolerance.
2) There are a few organizations that are explicitly pro WFH. If you're prioritizing WFH ahead of other things, look at doing something that isn't your ideal role and not at your ideal salary, but gives you the WFH goodness that you desire. Ideally, you pick an organization that has the sorts of roles (and money) that you'd ideally want, and you grow into that role within that organization.
3) When LinkedIn emails you and says "Bob from Google wants to talk to you", email Bob back and say, "Bob, I would love to chat with you, but I am only considering WFH arrangements. Please let your hiring managers know that there is good, affordable talent available to them, but who are unwilling to relocate."
I do this with every big name brand that contacts me via Linked In. I usually tend to tailor the message to something about how the business in question heavily relies on open source (and I name the pertinent technologies) and how those were developed via distributed engineering mechanisms, proving that such approaches can build world class software.
I hope people like me can create enough data points that eventually more traditional shops hear the "I won't relocate for you" argument often enough that they start entertaining people who demand remote work.
Anyway, my employer gets way more output out of me when I am at home than when I am in the office. I have a nice laptop, and everything is in source control or cloud fileshares, so I can move back and forth between office and home office easily.
My kids understand that when I am working, they don't come into the basement. I go upstairs and take breaks and hangout with my family, or take advantage of the nice weather. If I don't have scheduled meetings, I can shift weekend/evening tasks (like yardwork) to mid afternoon, when the bugs aren't as bad and the sun is shining. Email and code will be there during peak mosquito hours or when the weather is bad.
I live on an isolated 14 acre farm that is about 25 minutes from my employer's office building. Commuting isn't bad at all, but if I don't have to, why bother?