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How would you avoid ghettoization? Why wouldn't your rent controls just centralize poverty in the areas subject to those controls just as they are now? How would your idea differ from, say, the existing federal Section 8 program, which provides government subsidized rents based on the renter's income to private owners, where Section 8 homes already tend to be grouped together in ghettos?
Agreed.
I think the more modern approach is to use vouchers instead of direct support of the housing itself. So a typical Section 8 household would get a voucher to use anywhere (and the family could supplement the voucher to pay higher rent if desired).