It's not that simple. A lot of browser "standards" are standards in that they achieve the same end result, but for whatever reason they take a different approach to getting to that result, so you often end up needing browser specific code. This is especially the case with CSS, which is why so many "standard" CSS properties still need a "-moz" or a "-webkit" version as well, decades in. The only way the website can know if they're running the correct code for that browser is if they know what browser is being used, hence user agents. This is the reason that pop ups like this exist at all; sure they were lazy as fuck to not properly support Firefox, absolutely, but they wouldn't have needed to support Firefox specifically at all if browsers could just get their shit together and fix the "standards".

I would fucking cry tears of joy if browsers could standardize enough that writing browser specific code and needing the user agent was a thing of the past, but I really don't see it happening any time soon.