If everyone is a PhD computer scientist - then the wages of babysitting will rise to the true value of that service, and a babysitter will earn as much as a computer scientist. Currently due to abundance of availability of low skill resources - their wages don't depend on the value of the service and instead on their willingness to work for whatever amount to get the job, but once the resource scarcity becomes inverted their wages will be tied to the value.
Great. Since everything costs as much as a high-skilled computer scientist, no one can afford anything.
We're now back to limiting the economy because we don't have enough low-skilled workers. People are now forced to work suboptimal jobs for their skillset, and our economy stagnates because we're now fixing broken windows we broke.
Child care at least has an intrinsic value that will create wage equilibrium because it directly frees up someone else's time for high value labor. It should track closely to the income of the people you are serving, and it mostly does even in the US. This is ignoring the educational and social benefits that good childcare services can create which act as a future labor multiplier.