> I don't get why people are so keen on the per-hour model.
How many years have you been doing this? It doesn't sound like you've been at this for too long.
> I've negotiated fixed-price deals where I'm quite certain I can get the job done in x number of weeks
This works fine for a client who wants a very concrete x, y, or z.
There's a problem with this sort of client. They only want x, y, or z and after you give it to them, well, you're done.
If you have that sort of client and you're charging by the hour, you're an idiot. Quote them a fixed price at something like 500 per hour for what you estimate the work will take. They'll go for it, you make bank.
At some point in your freelancing career you're going to start feeling jealous. Of the "normal" guy. They guy who wakes up every morning knowing he has a full day of work and is working for the same person he worked for yesterday. He knows what to expect, how things operate, etc. Everything is stable.
Stability is an illusion, but it's a nice one.
At this point, you're going to start looking for clients who don't want x, y, or z. You're going to look for clients who need x. And some more x. Then some more x. They keep needing x and there's no end.
These clients are professionals. They know the industry. They're not really clients, they're middle men. They're agencies, marketing guys, whatever. They have a constant stream of work. They know it. And they know the best way to maximize their profit is to pay you by the hour. They will only pay you by the hour. They will laugh if you suggest anything else.
It's alluring to you, because you get a ton of work, all the time and you're still billing twice what you'd get working a regular job, and you still get to work from home, set your own hours, specify your own tooling, etc.
At some point, you'll get tired of this and decide you want to be the middle man. You start getting your own clients, hiring other guys to do the work ... and guess what? You're going to pay them by the hour. Because that's how you maximize your profit.
Now, I know there are one-man armies out there who have their own clients, bill fixed price, do all the work themselves and are always busy. I know they're out there because I used to do that. It's exhausting. You have to constantly keep marketing yourself, keep working of course, and wear a bunch of hats at the same time. At some point, you'll have the desire to "outsource" the marketing portion of the equation and that's when you'll start billing by the hour.