They would to multiple the prices multiple times to even discourage the middlemen, gentrifying at the same time the fan base, which is sad

It is, but it still feels better that the money goes toward the artist than it does to go to a middleman.

Reality is there is no good solution IMO, no matter what you do, someone is missing out. Just the reality of supply vs demand.

Perhaps it depends on your "Ship of Theseus" perspective, but we have all kinds of evidence that demonstrates music fans are quite often more than happy to see a live performance of a set of songs they've come to love even when not performed by the original artists. Look at how many bands are still selling out arenas even when original members are no longer with us.

Presumably individuals involved in these cases are already tapped out for how many performances they can do, so why not have other people put on the same show to expand the supply?

> by increasing supply

Er, I don't feel like you're thinking of what "supply" means here. We can't clone humans (yet). How many times do you expect a singer to sing in each city in a tour?

Jazz clubs book the same act for a week at a time. If there’s enough demand to fill a stadium for 4 nights in a row for a pop star, that sounds super efficient to me.

> but I’m curious why the artists don’t double prices to cut out middlemen

That is essentially what they have done. Ticketmaster is basically "We take PR heat to make you more money".