Lots of people are arguing governments should provide all citizens with an unconditional basic income. One problem with this is that it would be very expensive.

You are missing the point. It's cheaper to give the poor unconditional basic income than to have a huge bureaucratic administration that makes sure that they pass certain conditions to be eligible for welfare payments.

That might mean a low basic income but it would still be an unconditional basic income. Don't confuse the debate for a unconditional income with the debate about how high it or welfare payments to the poorest should be.

I guess this system to some extent exist - e.g. in many countries, the government does provide you with education and health care

Actually you are looking at the wrong countries. Countries like Iran would be an example where essential goods like food get's heavily subventioned.

There are many reasons why subventions are a bad idea. The produce incentives for companies to lobby heavily to be included. The encourage people to waste products that get subventioned. They need bureaucracy to be organised. The prevent innovation because new products usually don't fit into the template along with old products are subventioned.