There already are tax and welfare benefits to having children, and indeed it does incentivize having them when you really can't afford them. It doesn't seem sustainable long term, but we'll see. I don't think it's a problem with basic income any more than the current system. The bigger issue I find with basic income is that proposals typically don't include any mention of price control on the seller side and purchase control on the buyer side. Poor people are often trapped there because every local actor selling them stuff is trying to maximize rent extraction, and they continually buy things that are expensive and bad for them (case in point the recent cigarette article). Landlords get a lot of money from rent extraction, since they're paid in rent directly. It's even worse with universal, unconditional basic income. If as a landlord I hear everyone in my apartment complex is now getting an unconditional basic income of $20k/yr, guess what, next year rent prices are going up by around $20k, with lowered adjustments to account for other actors (like local food suppliers) also competing for this extra $20k/person/yr. This is basically the same thing that has happened to student loans. Without authoritarian measures to restrict economic freedom, which in addition to being authoritarian must also be good measures so as to not backfire as every other centrally planned economy has, basic income has no real chance at a large scale. In America in particular, authoritarian anything is a no-go.
A landlord may try to increase rent knowing that the tenants now have a basic income, however that creates an opportunity for someone else to provide housing at a cheaper price - it's no different from any other market, as long as you don't have massive supply-side restrictions like in some major cities.
The best way of fixing this is to make sure that there is an over-supply of housing (located NEAR the jobs) and to make it as easy as possible to move.
Economic incentives should encourage local, suitable (even for apartments) housing in an area to be approximately equal to the number of jobs in that area (then pad up slightly for BIG if that's also an 'employer').
