What would break is Javascript. The different browsers have been messing around quite a bit with their Javascript engines in recent years, and there are idiosyncrasies that have to be worked around. What you see as a minor change to how a browser handles a piece of Javascript does in fact mean that major corporate websites could suddenly no longer work for thousands of users.
When you have to support such systems, you want to be able to do testing to make sure that things work. This new scheme means that each and every day you are living under the gun, wondering if today is the day that Mozilla will release a version with a minor tweak that will leave you in a huge mess.
Unfortunately, although I've loved Firefox and have used it for years, I'm about ready to suggest that my organization no longer support it, because it's becoming impossible to realistically test against. The best that such testing can do is say 'It works today, but who knows about tomorrow?', which bosses REALLY don't like.