Because they're subsidizing the rest of the cost. But that's the issue. If you're going to pay that amount, why not just give the parents the money? Then if they want the daycare, nothing much changes, they just hand the cash to the daycare. Whereas if they prefer to raise their own kids and one of the parents wasn't working a high paying job to begin with, now you're not heavily subsidizing exclusively the option they find less desirable.
> I'm pretty sure that would leave us with extremely variable coverage for those who do choose kindergarten.
It would have a similar effect to having an economy that allowed more families to be sustainable on a single income rather than two. Then fewer of them would need daycare and there might be fewer daycares, but that doesn't seem like a great reason to force more kids into daycare, especially when the consequence would plausibly be something like the nearest one to you is 14 km away instead of 10 km.
> Although I am a free-marketeer, I also believe that these are services that should be available at quality to anyone independently of income.
But now you're talking about the price again.
Suppose the actual unsubsidized cost for providing quality service is X. If you provide a daycare subsidy for each child in the amount of X, it costs the government X, and then everyone can afford daycare. If you instead provide a cash subsidy for each child the amount of X, it costs the government X, and still everyone can afford daycare, because paying for it costs X and they received X in cash to use for that or anything else at their choosing.
> How is this perverse? Do we not need people doing low-wage jobs?
It's perverse because you're having the government pay e.g. $10/hour to subsidize their working a job that only pays $8/hour, when they could have done the thing the government is subsidizing themselves, had a $2/hour surplus if that didn't cost them the subsidy, and been happier because they get to spend time raising their kids instead of spending that time at a call center doing telemarketing.
And the way you get people to do the necessary "low-wage jobs" under those conditions is to pay them more.