Every engagement I run is fixed price. I get asked why often enough that I figured I'd write the answer down properly once and then just send people the link.
Hourly is the default in this industry and it suits the person doing the work more than the person paying for it. If the job runs long, they bill more hours. If it runs short, well, that was the rate. Whatever pressure exists to get finished sits entirely on the client's side of the table. I don't think most agencies are being cynical about this. It's just where the incentive lands if nobody does anything about it.
With a fixed price, if I'm slow that's my problem. I put the number on the job, so I've taken the risk on it. The client knows what they're paying before we start and it doesn't move unless the scope moves. When the scope does move we agree that in writing before I change anything.
The pushback I get most often is that you can't possibly know what something will take. That's fair when the scope is vague. It's much less true when it's specific. The scoping call is where I work out which of those we're dealing with, and if we're still in the vague version then I won't quote. Which is usually a useful thing to find out early.
People assume scope creep is where fixed price falls over. My experience has been closer to the opposite, because every change has to come up as a conversation instead of quietly getting absorbed. Can we add this becomes yes, and here's what it costs, or here's what would have to come out instead. That makes the trade-off visible, which makes it easier to decide.
Part of this is also just about not putting myself in a position I don't like. I've watched people stretch easy work to hit an hour minimum. I did it myself years ago when I billed by the day. It's not good for the work and it's not good for how you feel about the work, and a fixed price takes the option away completely.
Things I don't do: monthly retainers, design subscriptions, unlimited-revisions packages. They work fine for plenty of agencies. They don't work for how I run this, which is one project, one outcome, one date it's finished.
If you're weighing up hourly against fixed price, the question I'd ask is which one makes the behaviour you actually want more likely. And if what you want is open-ended exploratory work with no defined finish line, neither of them is right and you probably want to hire someone.