Isn't it the opposite? It fills the gap by providing poorer people free child care where richer ones can afford it by themselves?
Means-tested only makes sense if you have a progression instead of a hard cut-off, otherwise it creates these pits of despair.
It's similar with welfare in Germany: if you have an extremely low-paying job, welfare will "top up" your income up to the same level as someone with no job. So until you break even, working an extra hour or taking a job that pays slightly more is economically pointless because it has no effect on your bottom line: every extra Euro you earn gets deducted from the welfare benefits. This encourages undeclared work, losing the government money via taxes.