>Now people are saying that we should put all those things in one basket and hope that the politicians don't screw us over later?

Having one basket for everyone is politically easier to defend.

If you look at the Finnish or Nordic welfare model in general, most of the income transfers go to to middle class who also pays for them. Poor people are taken care on the side.

The reality is that people don't care about poor, but if you create system were everyone gets money equally, people don't want to give it up. We already have kind of UBI for children in Finland where government pays certain amount of money every month for families with children, rich and poor. Nobody wants to give it up, because free money (paid by taxes).