Which Aperture Should You Choose for a Lens?

There is 1 advantage of a wide aperture that you didn't mention.
You did talk about it indirectly, of course, and that is low light.
And then the advantage for AF, which always works better with more light than with less. Even if you don't need f2.8 for the photo, a lens with f2.8 can still be useful because of focus. Especially in somewhat more difficult lighting conditions, when there is some action.

Follow-up question. Is there also less glass in a less light-sensitive lens? In other words, what determines the showpiece of a lens? I'm curious about examples or how you know that the sharpness of a lens does not fall short.

As usual, clear and 'to the point'.
Those large apertures were much more important in the film era, you could barely get ISO 800, with grain and shifted colors, so you had more need for fast lenses. Now that you can go up to ISO 3200 or 6400 quite well with most cameras, that need is much less.
As a Nikon Dx user myself I only have 2, a 35 that I simply wanted to try and a 105 Macro (Nikon says micro-nikkor). The latter does have added value, because you lose light sensitivity when you get that close, and movement is extra damaging there. ( With those lenses they fiddle with the focal length, it is actually a kind of zoom lens)

At the shortest distance it's still 4.8, one and a half stops less, not spectacular, but if it started at f4, then it would be a problem.

People often choose a smaller aperture number because of the depth of field. As you say, the distance to the subject and background is also important. Another factor is the focal length being used. Try standing in one fixed spot (tripod) and take a photo with your widest angle and your longest telephoto, choose the same aperture for both, you can also take a photo with both your largest and smallest aperture. Then look for the differences. You will see that your aperture number has hardly any influence with the wide angle, while with your longest telephoto you can clearly see differences.

A lens with a low f-number doesn't always have to be expensive. I have a Canon RF35mm f/1.8 and paid something like a good 500 euros for it new back then. A great little lens for portraits, the city or crowds because it's small and light and you don't stand out with it. One downside is that you shouldn't walk around with it in pouring rain.

The Sony FE 20-70mm F4 G lens is an example of an F4 lens with beautiful results, nice and light, reasonably compact and a super travel lens. Together with the Sony A7V a perfect combination where you really don't have to be afraid to turn up the ISO value. Still bothered by noise afterwards? Then Lightroom Classic and/or Topaz Studio are your friends.....