Your argument here is essentially "if the government wants to lease out the operation of a public good to the private sector then it has to be a long lease because otherwise who will put up the capital to take that on". And it's true!
But I think the underlying point is that maybe we just shouldn't do that? Our governments should be able to competently administer things like parkland and street parking. And the cost of giving up on them doing that is unacceptable because as you say, you can't do it without giving up control for an intolerable length of time. So sure it's necessary to do that if you're gonna do it, but that's precisely why you absolutely shouldn't do it, it's an absolute dereliction of duty.
Why should the government administer an airport terminal? It is ultimately a place for private businesses (airlines) to have reception and waiting rooms. I'd argue that the airlines should be buying their own land and building their own airports. Of course it makes sense (except maybe the busiest airports) for the different airlines to share a runway, and so it start to look like a public place. Airports are not public places though, and so I don't see why local governments should administer them (the FAA does have some safety operations at an airport).
While your typical playground makes sense for the city to administer, if the park is really a zoo it makes more sense for the city to not run it at all. However since the city benefits from the zoo it does make sense for the city to help the private zoo get started in a good location.
I don't really disagree that much with your point, but I'm also thinking it needs to go into the "Sure, and I'd like a pony" bucket.
Point being that municipal governments have tons of responsibilities: airports, parks, health districts, roads/sidewalks, etc., etc. There is just no way they can be competent in all these different areas, and indeed they aren't. There are good examples of non-profits that manage public resources much better than city government can, at a much lower cost (the Trail Foundation in Austin comes to mind for me). We shouldn't throw away the baby with the bathwater.
But I think the underlying point is that maybe we just shouldn't do that? Our governments should be able to competently administer things like parkland and street parking. And the cost of giving up on them doing that is unacceptable because as you say, you can't do it without giving up control for an intolerable length of time. So sure it's necessary to do that if you're gonna do it, but that's precisely why you absolutely shouldn't do it, it's an absolute dereliction of duty.