I would go further and say that the annual payment amount should be set by a feedback loop, so the incentive rises every year that the birth rate remains below whatever target (eg. replacement), and stabilizes as it reaches that target.
At some point, would-be parents at the margin decide they don't need a job to attain economic security.
This is basically a way of doing price discovery on the "market rate" of parenthood. Currently we're under-paying and getting the predictable outcome, and we're all out of ideas.
(In fact, I think this should basically be the solution to all labor shortages, of which parenting is just one example. The wage should increase until the market rate is found, even if that wage is much higher than people say it "should be").
That is the solution used for most labor shortages. Typically when people talk about "shortages," they actually mean something where the market price is higher than they arbitrarily think it should be.
It's the correct solution, but I'm not sure it is put into practice so universally. In some fields, yes, but in others the offered price is quite stubbornly anchored and the people with the authority to increase their offered wage seem to prefer to shrug, complain that nobody wants to work these days, and then go out of business, rather than continue increasing their bid until the market clears.
Just the other day there was a thread about how Zeiss is the production bottleneck for ASML and can't scale because they are running out of glassworkers, because nobody wants the job, because it doesn't pay enough to make up for the lack of job security.