Similarly, if we allow illegal immigrants to rent flats then that will also push rents higher. Should we attempt to prevent this as well? If not, why not?
Maybe put another way, illegal immigrants are part of the community, so their presence in the housing market must be balanced against their role in a more complex system.
But if you are just asking about the nature of Justice, I don't have any thoughts on that.
There are lots of factors that impact housing supply and demand. Whether they should be regulated / stopped generally becomes a question once the public actively engages in discussing it (see foreign investment in the Pacific Northwest for an example).
Basically, if the public doesn't care, the politicians don't care. Since a pol's main incentive is to get re-elected, the issue has to become important to their constituents, otherwise it effectively doesn't matter.
GP wasn't asking whether it would be prevented, merely whether it should.
If anything, the people who don't want to compete on price with AirBnB are the ones who are rent seeking.