Yes. But the presence of a large group with a consistent fixed income would incentivize the building of large-scale low cost apartments - those don't exist currently outside of major cities (where 'low cost' is substantially higher), because the demand isn't there.
There is no shortage of incentive for that in most of western Europe - such property is significantly profitable. The reason why not much gets built is because (a) cheap housing blocks results in ghettoisation, which most governments try to prevent with mixed-dwelling planning requirements, and (b) local residents invariably object to any planning request for housing more low-income people near them.
I've seen enough uncompleted estates and empty unsellable new buildings over time to suspect that such property is significantly risky.
Maybe such property is significantly profitable today, but we can't be sure by the time the building is complete.
I suspect it's more likely a simple business decision: the profit doesn't outweigh the risk.
In London, construction companies work hard to avoid the commitment to affordable housing and pay councils bribes to overcome that. Why would they need to pay councils off if this was a profitable option for them?
London's a special case: every single unit that can be converted from "affordable housing" to "luxury accommodation" is a massive profit realised by the developer. You can make a lot of money from building low-cost housing, but you can make an awful lot more from building really expensive housing, because there is essentially unlimited demand for both.
