Correction, that's not "conservative popular opinion". As with many surprisingly conservative elements of Dutch law and culture, it's the result of the coalition-based politics where "non-essential" concessions are made to the (socially, not fiscally) conservative minority.

Basically the "stuff that isn't worth fighting an election over". See also: drugs (we're now falling behind, and even moving backwards), opening hours (most of the country still shuts down on Sundays), or to give a recently newsworthy example: insulting the royal family being illegal.

Mix that with the dominant right-wing urge to "privatise all the things", and subsidised child care gets happily thrown under the bus by various coalition governments, despite what the majority of the population actually wants.