I prefer other forms of contraception since abortions are kind of messy and are health risks without antibiotics, which is a reality we may have to face in a few years. Something like giving out money to anyone who takes a contraceptive shot that makes them infertile for a year is more my preferred approach.

Most of the people who take such an offer would be people who didn't intend to have children that year anyway. It wouldn't be any more politically workable than your proposal though since it would really strongly hit anti-eugenic heuristics.

The advantage of abortion is that there is a set of people who do have abortions yet have high enough time preferences that they don't end up using other kinds of contraception as much.