That's exactly what the EITC is. The main benefit is that it's a direct subsidy by the government instead of burdening businesses with paying people above what a free market demands.

From a political standpoint. It's also a lot easier for people to support. You have to work to receive it and it's been popular in both Republican and Democratic administrations. I can't speak for the current one. I don't think Trump has any core set of beliefs.

Over 60% of government benefits go to the employed. Walmart has built a whole business model around this, giving workers information on collecting government benefits, which is essentially a huge government subsidy for Walmart and similar businesses.