Question is where do you draw the line? How is it any different to paying for somebody else's children?
If we all get state schooling offered to us up to age 18 then we are all on a even level in terms of opportunity. Start paying for peoples adult choices then things become incredibly unfair as not everyone will want to go, be academic enough to go or even require to go (some jobs/careers just do not require degree level education!). What about paying for plumbing courses, certifications, tools etc for tradesmen?