There are many spaces that can be maintained either publicly or privately that when privatized don't always result in the best outcomes for consumers. A good example are private utilities.
I had a relative that sold his house in a municipality in east Texas and moved to a new development in central Texas. He intentionally chose a house just outside the nearest municipality to avoid paying local taxes. It all seemed great until he got his first water bill from the private water company, only to find that his water bill was astronomically higher (2.5-3x more). His other private utilities were a little higher than what he paid previously, but he was particularly upset about the water.
The water company isn't some multinational corporation, but they have a profit incentive, zero competition, and they control the water infrastructure, so the community there doesn't have much leverage in that scenario.
On top of that, public utilities are accountable to the public, while private utilities are accountable to shareholders. There were no obvious economic reasons for the incredible disparity in price, other than one utility had an incentive to profit while the other didn't.
As long as those organizations are not for-profit companies.
Plus it is becoming increasingly risky to engage with for-profit companies for certain things because of their insatiable desire for data on their customers.
But those are pretty much all the remaining hard problems! If it was self-funding and didn't have any opposition, someone would be able to solve it.