> This is a very smart way to organise society, if we think about it: people have to do more and more work to bid against each other for the limited amount of resources.

It's a very smart way to organize a society if you're a landlord using artificial scarcity to extract rents equal to the productive value created by everyone else. For everyone else it's warm dung.

It's not even economically efficient because it undervalues non-wage labor, of which child rearing is a prominent example that we are now under-producing as a result.

> reimbursement for all kids related expenses

Reimbursement overcomplicates things for no good reason and creates a lot of perverse incentives to overpay for services etc. Just choose an amount per child and make that the amount of the child tax credit.

But that's somewhat separate from the main thing driving the competition, which is artificial housing scarcity (and artificial scarcity in general). That may be the single most pressing problem facing us today, outside of climate change.