Well, the actually wealthy and well off people will just hire an immigration lawyer and fly there while keeping some wealth, and not working their way from dangerous predicament to predicament one step at a time, often dying in the process.
If you’re well off, you sure arn’t going to give it all up to a smuggler for an asylum claim.
But outsourcing them to an collection of independent bureaucracies(companies) is so much more ‘efficient’ than one bureaucracy just building what it needs to.
Besides, the government owning and developing housing would just be a huge cost to the taxpayers given how unprofitable it is to own or sell real state. Why the government could even build enough to actually house all the people on housing and then rent the surplus public housing out at below market rates but above cost to build in order to help fund the service, and that sounds like it could cut into the profit margins of the poor landlords.
Nope, better to make a deal where the government assumes the risk for the project if a project fails, and the corporations get to take all the extra profit if a project succeeds./s