Why do all browsers' user agents start with "Mozilla/"?

Reason for this are the infamous browser wars.

In short - browsers started to pretend to be some other browser, because some websites served content based on which browser asked for it and they also wanted content meant for other browsers.

I find it surprising it still haven't been solved to this day. Since userAgent can't be safely removed for legacy reasons, why some new feature clearly identifying a browser wasn't introduced? Yes, most of the time you don't need browser detection, but rather a feature detection, but it is not built-in JS neither!