> Luxury condos reduce demand on other buildings, helping keep rents down. Without them you'd have more rich people bidding on regular stuff.

Luxury condos attract rich people that otherwise might not be in the local market, both directly (to live in the condos) and indirectly (by stimulating a local increase in services catering to a rich clientele, making the area, not just the condos themselves, more attractive to the rich.) This can make the net effect an increase in demand for other existing housing from the rich, rather than relief of such demand.

Attract rich people from where? If the presence of rich people is a problem then solving the "problem" by keeping your neighborhood shitty just means the problem becomes someone else's to bear. It doesn't actually solve it. And notice that if they "solve" it too then you get rich people in your neighborhood driving up your rent and you live in a shitty neighborhood.