If you have more fans than seats, some people will be unable to attend. That's unavoidable. But the constraint you're replying to says "ensure that fans without a lot of money can see me", not "ensure that all fans get to see me". So your criticism is a little off target. Yes, those fans willing to show the most dedication might have an advantage.
But we can solve the majority of the "disproportionate power to the wealthy" by the simple expedient of only allowing one or two tickets per person, and matching ID to purchasers of the ticket at the door.
In this app, allow the user to collect a free sweepstakes entry, with a 60 minute cooldown timer, to a maximum of 8 entries per calendar day. Whenever concert tickets go on sale, reserve a block on the floor from the Nth row to the back of the floor. (We all know that the spots all the way up front are for the groupies, superfans, and rich people.)
Allow users to allocate their entries to specific shows/venues on your tour. Hold a lottery for each show, and allow the users that are drawn to buy 2 tickets for $2, and an exclusive concert tee for $21. Allow a few winners to get gratis superfan passes, to meet the band, collect autographs, get the gratis ultra-exclusive VIP concert tee, scream and collapse on the fainting couch, or whatever it is your hardcore fans would most like to do. Close to concert time, if the venue is not actually sold out, do another lottery and make a second-chance offering to get any previously unsold tickets for $1 each. Any user that does not or cannot buy tickets can then spend their entries to get gratis/discounted merch or media files, or just get their remaining sweepstakes entries back, perhaps to try again on the next show.
The user arrives at the venue, and presents a certain screen of the app on their phone to be permitted entry.
This rewards dedication to the band (and its licensed merch). In order to maximize your chances, you have to check in every hour that you are awake and not at work or in school. You can't get those tickets any other way, and if you don't make the effort, someone who is more into the band will.
Also, the app itself can recruit and assimilate new people into your fanbase. And you can make sure that the band's own holding company controls the IP and app-based revenue, not the record label, promoter, or distributor.
You can realistically expect your real fans to buy one tee per tour. Farmer accounts will likely show maximum sweepstakes entry activity and no game-play activity until winning a lottery, then will refuse all the merch upsells and never be active again. You can just dump those user ids into the "ignore" bucket and rescale your reserved bloc so that there are still enough seats for the real fans.
In any case, why would anyone buy a transferred fan club burner phone instead of a transferable dollar-priced ticket from a scalper? Why crack the proof-of-fandom test for a single artist, when you could break the CAPTCHA for all of Ticketmaster? The hypothetical attack you imagined requires greater effort and produces less profit than if you were just a regular ticket scalper.
Which fans without a lot of money? How do they get picked? Lottery? Who can click the fastest? Who has no job and can stand in line for days?