[...] it doesn't account at all for how badly someone wants a ticket [...]Only given that there a lot less rich than poorer people it seems pretty unlikely that badly wanting a ticket would correlates with being able to spend a lot of money on a ticket. And I would actually suggest that the extend to that people would like to buy anything is mostly independent of their wealth. Why would a poor guy be less interested in owning a private island than a billionaire? There are just a lot more things in front of an island that they have to take care of first.
[...] and to whatever extent it might be gameable, the poor will always be the least well-equipped to game it.
Certainly true but that is not an argument against a lottery because it applies to most if not all systems.
Also, while you can't clone Taylor Swift and put on 10 shows at once, if the full market value for popular tickets went to the people creating that value (instead of resellers), there are actually lots of ways the market could respond to increase supply. Taylor Swift could do more shows per city. Or more shows per day. Or livestream to multiple venues. Or build extensions on the venue. Or build new venues specifically for this kind of thing. The list goes on.
As far as I can tell being on tour is a really tough job. They could maybe have two or three sets of the equipment with separate crews and cut down the time between shows but that will take you only so far. Also being close to the stage is very different from being a hundred meters away or only looking at a screen. There is certainly some room but I don't think it is that much. And in the case of sports events it is certainly even worse, you can't have games every day or so.
Besides that, the argument that a smaller share for resellers and a larger share for the artists could help in the way you mentioned is not limited to any specific distribution strategy and applies as well to a lottery-like scheme.
A giant band can't be duplicated exactly, but they do have lots of competition. They compete with other bands, the movie theater, a quiet night in, the bowling alley, etc. It's entertainment. So if floating ticket prices put the tickets out of reach of most fans, the market will find a way to increase supply.
Sure, you can always do something entirely different, but we are discussing ticket allocation for a specific event. Doing something else if you can't get a ticket is not a solution to the problem.
Otherwise the average fan goes bowling, and long term you lose your core fan base. The supply will increase to meet the demand. Maybe via one of the ideas above, and maybe via something that we can't even think of right now (and which someone will get rich for figuring out).
As said before, I am not convinced that the supply side is elastic enough in this case. Personalized tickets and lottery-like sales are actually things that quite a few bands and events do in order to keep the price under control.