It’s like “Have you tried turning it off and then turning it on again?” Yes, yes, and I tried that, too!
And the reason why this is a universal T1 tech support tactic (to the point of being a meme) is because there are plenty of times that this does do the trick. Definitely not all the time, but as someone who worked in internet tech support at a call center the solution often was "Unplug the modem, unplug the router, give me a moment to do something on my side (which sometimes was nothing - but it made sure that they actually unplugged it), now plug both back in".
And before someone jumps me for lying about the "do something on my side" part, when you can clearly see someone's port uptime is 200 days despite them claiming they reset their router minutes before calling in, you tend to learn very quickly that people lie (or are wrong/misinformed) whether that's intentional, or because they thought they unplugged their router but instead unplugged their PC/monitor/etc - the end result was the same. We had customers on all sorts of different infrastructure, some of them I could do a port bounce from our end (and I did for those cases), but others the customer had to unplug it from their end.
So even if the troubleshooter only fixes say, 25% of people's problems - that's still 25% of problems resolved right away, and without needing to go search online. I do not think I've run into a Linux distro that has any sort of built in troubleshooter that could at the very least help those 25% (or whatever the actual percentage is) cases.
About the bonus peeve, it's definitely a double edged sword for me. I know exactly what you mean, and I hate those moments.
But at the same time, one thing I've come to dislike on GNOME is when I click a link in Thunderbird expecting it to open right away, and instead get a "Mozilla Firefox is ready" notification. It makes it feel a bit clunkier/slower when I've come to expect that interaction to be instant (and I wouldn't be surprised if that's precisely why it hasn't changed in most places).
So now instead of being bothered by one case, I get bothered by both cases lol. I wish there was more of a middle-ground, like middle clicking the link (or holding control/some other modifier key) would bypass that notification and just directly open/focus it.