Well I for one am always in favor of arbitrary humans having better ways to voluntarily attenuate their own fertility, full stop.

We may have a depopulation shock problem on our hands at the moment, but trying to encourage more accidental births isn't the way to solve that: we need to increase social and financial incentives for forming families and pull away as many of the social and financial barriers thereupon that we can. Not to increase population but to better slow the free-fall of it decreasing so badly that it upsets the actuarial tables.

While I have no way to assess whether better male birth control options would directly positively impact education in particular, I see zero ways it could negatively impact it.

Some problems suffer negative economies of scale and simply cant be outsourced.

There is not enough money in the economy to pay for all the domestic work that productive people do for themselves.

Parenting is a good example of this.