I think it's distinctly possible that the current status quo may cause an overreaction. Feature detection is good. But we may also need the ability to do specific version checking sometimes.
What I think would be best is two things: A feature advertising string (preferably with some versioning in itself), and a new User Agent string that is just that: The user agent. As in, "This is Firefox 72.2.813". Maybe the OS in there too. I think a non-trivial part of the problem with the UA today is "Hey... I'm Firefox. Also, I'm Mozilla. Also, I'm edge 3, and Internet Explorer 6, and today I think I'm also Chrome. Also, I may be a monkey with a banana plugged in to an ethernet cable." Part of the problem is that people abuse the user agent, but part of the problem is that the user agent string is also a pack of outright, outrageous, self-contradictory lies. A truthful field may still have significant utility.
One of the things I've learned over the years in software engineering is that you should do you best to make sure that your system doesn't contain lies, or, failing that, treat them like any other issues that you should contain at the edges rather than letting it run riot through your system. For instance, if you decide to let customers have 10GB of bandwidth free before you start charging them, you should never accomplish that goal by tweaking the bandwidth counting system to report 7.5GB of usage as 0GB. That is a lie. Tell the truth about the usage and let the billing system apply the discount, which is itself a truth as well. You always pay for lies in the system in the long run. It is a very common pattern in coding as well where some function author figures out how to assemble the correct lie to some other function to make it do what the author things they want, but in the long run you're better off telling the truth and fixing the code to work with the truth. Otherwise, well, you really do end up with a tangled web of code. Which is... exactly what we've gotten with UA-detection-based code. We won't necessarily get the same mess if there's a new UA that isn't a lie.
I'm not claiming this will lead to utopia. Minority forks of popular browsers will fail to pick up the necessary ad-hoc bug fixes this way, for instance. My claim is more like in the long run, the best thing for everybody is just to have a user agent that tells the truth, even if on occasion in the short term you experience occasional problems.
(One way to at least partially achieve this is to standardize the new truthful agent string to something like (\w+) ((\d+.)+\d) (\w+), and specify it as "non-conforming true user agent strings MUST be entirely rejected and treated as being absent", so anyone who tries to be Firefox and Chrome and also a monkey ends up being nobody in particular.)