Exactly, when the state pays the maternity leave, it doesn't create a disincentive for the employers.

Should be obvious, but somehow is not. Even if you make laws like "the employer cannot ask about ...", well, they cannot ask, but they can still make a guess, right? (And then make up an excuse, because guessing is also illegal, of course.) Instead, if the maternity leave is paid by the state, the employer does not bear the cost, the mother doesn't have to worry about the employer going out of business during her pregnancy, etc.

Generally, as a rule of thumb, if the "society wants" something, it should be paid by taxes, not thrown as an additional burden of the employers. That way, employers are incentivized to try to avoid the extra costs by doing things that are socially wrong, and the employees are not dependent of having a good and wealthy employer, and even the unemployed can get the same benefits by the same channels.

For example, if you want to prevent crime, you don't say "the employers should provide police to protect their employees", but instead you pay the police from taxes, and leave the employers out of it. Exactly the same logic applies to health care, parental leave, etc.

Not arguing either way, but there is a natural disincentive for employers to have to plan around their employees being gone for those long periods of time, plus the ramp-up time upon their return, depending on the job.