I use Firefox and haven't run into this problem. I guess I've been lucky. Why Firefox rather than Chrome? On my Google Chromebook (original Pixel), Chrome (the last versions I tried) are almost completely unusable - it hogs all the CPU until it crawls to a stop and needs to be killed. Even if they fix that, I'm not going back, however, because Firefox's handling of text is so immensely superior. It was bad years ago¹ and it's still terrible. One contemporary example: hyphenation support.
Google products, which I can't get away from, are starting to fail completely on Firefox.
I've run into several other complex sites that fail on Firefox. It's sad, because I've used it for years. I'm using it right now. But my default just switched to Chrome because I started having too many Firefox issues.
The real problem is not that Firefox has issues, but that it's a small enough market share now that more and more web services can get away with not bothering to test on it.
I hate how, as a web developer, I've probably been part of the problem. My workflow has somehow ended up being 'do everything in chrome and only at the end test if it all works in firefox and safari'. More than once I forgot that step and ended up making small fixes for Safari on request, but not Firefox because nobody reported issues.
Once I became aware of this, I've been trying to be more diligent about thoroughly testing things on Firefox.
I wonder how many other developers are in a similar situation, where Chrome is their default browser and/or their main debugging environment. Part of the problem for me is that I find the Chrome dev tools superior, and that makes it so much easier to just forget about the rest (not that I'm justifying my behavior, btw).
I generally like Chrome dev tools better, but Firefox (and Firebug, RIP) has some unique tricks, in practice I use both at times. But I agree a lot of people take your approach of Chrome as default, Firefox/other for testing, and that's part of the problem. (If you haven't heard of Selenium+SauceLabs, they can help with your automated testing of multiple browsers.)
I still use Firefox as default, both for developing and for general web browsing. It and my set of extensions fit my preferences too nicely and have no equivalent in Chrome. I use Chrome at work primarily for Google Hangouts / Meet, the occasional debug session, or just to have another session. (Trying to get into Chrome's Profiles feature too.) At home I just use Chromium from time to time, mostly because my computer is starting to age and I notice the performance difference for certain things.
Why not switch to developing in Firefox, like, now? As long as the debug tools are usable, why throw out the baby with the bath water for getting a tiny bit more a tiny bit sooner? Let's have some love for our future selves..
FWIW, I'm exactly the opposite. I dev on firefox, only bother with chrome at the last minute (although I'll check it's responsive mode a little earlier) and get somebody else to check safari.
I think Firefox's Developer Edition has been providing better dev tools than Chrome for some time. But then I've never been entirely happy with Chrome's Dev Tools having grown up on Firebug and relatives for Firefox. But then I've never liked Chrome and I only have Chrome installed because my corporate environment has become one of those that mandates Chrome because that's the only thing IT at large can be bothered to test for internal facing sites. As a developer of externally facing sites, I laugh/cry in their general direction.
(Also, I think a lot of people discount how good Edge's Dev Tools have gotten. There too my corporate mandated environment is mostly stuck with Windows 7 and an intentionally broken IE 11 due to Oracle and using their terrible software internally.)
It's so weird (I don't know if you've left this thread or not). I'm working on a virtualbox linux at home and chrome doesn't work on drop-down menus. I only discovered this because I was trying out a browser called vivaldi (which I really like but it has chrome dna) and it didn't work there. So I tried chrome and- indeed- it doesn't work in chrome either. Works fine in firefox.
Upon googling, I discovered that drop-down menus have been an issue in chrome (even not using vbox). I'm using zurb foundation for the menu js/css, fwiw.
The real problem is not that people don't test on all browsers, but that people have to test, still, on multiple browsers. The standardisation does not work well, new stuff is out constantly, vendors not independent experts control the process.
Firefox is my next item up the chain if PM has trouble. Trouble with individual browsers isn't my biggest problem; my work blocks so many things. Youtube has stopped working. Most of the cool ShowHN demo projects don't work (when they do once I get home, I mean).
I find that Firefox works well enough for my normal need. My other two browsers are SeaMonkey & PaleMoon (sense a pattern?). The only alternative browser I use is Links.
The most specific example I can think of is the sears credit card site, I couldn't pay the bill with Firefox, so I keep a Chrome installation handy for the occasion a site doesn't work.
It's even worse. I would sometimes accidentally write infinite recursion in chrome and it would lock the computer. I think this happens if your recursion involves the DOM because chrome unsafely uses privileged resources to accelerate layout. The same code in Firefox would only slow to a crawl and be recoverable.
¹https://lee-phillips.org/google-chromeBadKerning/