Its already here with some stuff, look at the sheer amount of cruft built into web browsers. You can't break existing sites, allegedly, but that just means that some things are set in stone never to be fixed.
In the year 2323, browsers will still have to say "like Gecko" to maintain compatibility with websites that won't exist and no one would miss even if they remembered they existed.
There are still websites built on top of scraping the output of a virtualized IBM 3270 terminal connected to a virtualized IBM 3274 terminal controller connected to an I/O channel on a virtualized mainframe running CICS on an MVS virtualized on VM/370 hardware.
So browsers are hardly even a bump yet on the cruft already accumulated.
In the year 2323, browsers will still have to say "like Gecko" to maintain compatibility with websites that won't exist and no one would miss even if they remembered they existed.