I think Firefox for a long time tried to optimize for those users who do want to tweak their software, and doing that can even be a way to make superior software (instead of aiming for the lowest common denominator), but it is certainly not the right approach to maximizing _web browser market share._
I didn't use Firefox for many years (because I thought it sucked; slow, bad defaults, always apologizing in this anoying way for having crashed the last time I used it) but I now use it every day again (though not as my default browser; I tend to keep all the major ones open) and I'm glad to see Mozilla recently seems to have changed their priorities and focused on usability and performance. I hope it's not too late.
> I would even expect if I quit browser with something written in the address bar (or search bar, etc), when it starts up again, it should be able to preserve this half-entered user input!
I'm pretty sure no one expects nor wants this. You're definitely in a minority here. The problem you describe isn't very technical, it's simply that you want something else than most people else and you don't want to take the time to configure your browser to how you want it to behave.
I think the lack of improvements in desktop UX in the last 10 years is making every desktop OS to slowly adopt mobile UX conventions. Some of those new conventions are a step back.
Personally, I don't like it when browsers implicitly keep tracking things when I close the application and then fire up some half-baked version of the same stuff when I come back later. If I want to remember where I am, I can easily bookmark some or all of my tabs.
Firefox has had a particular problem in recent versions where it seems to think it crashed on the previous shutdown, even though there was no user-visible evidence of this, and then tries to restore the previous session even when it otherwise wouldn't. That's not helpful if your previous session involved shopping for surprise Christmas presents for the SO who is now standing behind you as you open the browser again several hours later for some entirely unrelated purpose, in a totally hypothetical example.
I wouldn't expect this at all!
But Chrome will quietly exit, and when you start it next time, will offer to restore the tabs that were open last time. Chrome approach wins, hands down.