There's no tuition in Swedish private schools? No fundraising rallies? No private donations?
And yes, capitalism is horrible for basic necessities that everybody needs. Instead of having to compete on product quality, they just rely on people having to use their product to gouge them while also pressuring providers because of the guaranteed business they are managing.
Capitalism is almost fine for luxuries for example. The small pool of people able to pull off the required product quality means that they are well-compensated while people too poor to buy these items can fall back on cheaper bootleg.