In general I share the desire to make the tags list more useful/easy to use. Unfortunately it is in good part out of our control, limited to what Discourse (and plugins) can offer.
I had looked at these settings previously, hoping to improve things in certain respects, similar to what you suggest. I just discovered, though, that there was an unclearly labeled/described option which actually does affect the number of tags that show up in that list. I have now set it to 50, so hopefully it is now showing all of them (I didn’t count precisely, but it’s certainly more than it was).
However I am unconvinced that a popularity-first approach to tag presentation is actually the best way to present tags, for a couple of reasons. First, the most popular ones are also more likely to be the ones people can easily think of and remember. Second, showing them first in the list will tend to prioritize those for selection, even if they are not the best match for a given issue report or feature request. And making it non-alphabetical makes it harder for people to sensibly scroll through the now-complete list to find some option in mind. I think if you consider the total opposite approach you might see what I mean: what happens if you show no tags there and it’s just a search/entry field? People will likely type for what they would use to describe the area of functionality it is, or whatever else they might want to tag it with. Ironically this encouragement to search could actually result in better matches in many cases, as the autocomplete shows them the tags that are close to what they’re entering.
That said I want to be clear: I do not think the current tag display is ideal, and I do hope it is improved over time. For now, we do have the option to choose between popularity-ranked or alphabetical. Previously it was alphabetical and I have just changed it to popularity-first, so let’s see how that goes.