Existing certificates issued before a certain date will continue to work - that's the solution that Apple, Mozilla and Google have proposed and/or shipped (all of them - no reason to single out Mozilla here, they're just the only ones operating an open/transparent root program.) Not sure what you're referring to about the separate program?
This doesn't make any sense. First of all, some encryption at the cost of risking that these obviously broken CAs continue to mis-issue certificates is definitely not better than none. Browsers might as well accept self-signed certificates if that's how they run their root programs.
Second, both Google and Mozilla are Platinum sponsors of Let's Encrypt, and they've made this decision. Are you saying they've been manipulated by other CAs, or that they themselves (somehow?) work for them, or get paid by them? Also, if that strategy would work, why aren't CAs constantly trying to get rid of competition that way?
It's important to see past the inconvenience that a particular change is causing and consider all the factors. Browser vendors have already gone out of their way to make the impact for existing users of these CAs as small as possible, some of them have helped establish Let's Encrypt, etc. They can't take care of everything.
This is just a backend issue - there would be no impact on browser compatibility. They don't even have to upgrade Java, just modify their trust store.