I like development in Firefox too. When I was doing it intensively (just ~2 years ago), I found some of the CSS I was using behaved differently between Gecko, WebKit and Blink, though (and differently again in Android's pre-chrome browser), so I reconfirmed that I do need to test some things across all browsers. By differently, I don't mean prefixed browser-specific CSS (although there is that), I mean standardish things like table row height calculations showed up significantly differently, certain border highlights, and a number of WebKit rendering bugs that Gecko did not have. Key-event based text editing and wheel events are also significantly different, even more so when you include the common mobile browsers.
Given the megabytes of JavaScript on many websites, the chances that some of it depends on some random VM internal quirk is quite high.
In my experience, unfortunately it isn't true that apps work with very high reliability. This is why I use multiple browsers. I don't want to use Chrome, and I encounter new websites with functionality that don't work properly in Safari or Firefox quite regularly. Some of this is even quite basic functionality.
From things like shopping carts where the final payment button doesn't work in Firefox (nothing happens), to video conferencing that sort-of works in Safari but then the audio breaks while it is reliable in Chrome.
Even GitHub doesn't render properly in Safari occasionally (the page is full of weird size text and giant rectangles). But that's almost certainly a Safari bug.