Except for the whole launch facilities thing they lease from the government.
More likely they lease launch facilities from the government to minimize regulatory interference from… the government.
But you know it ISN'T private, because every rocket ever designed will end up in public space, either literally in outer space, or dropping parts in the ocean, or a tiny tiny tiny tiny chance of exploding somewhere less convenient.
This idea that you can just make your own little closed off launch pad and therefore ignore society is stupid.
Some of the more onerous pushback comes from people who have been ignored before and turned out to be right. For example, when Dupont and friends first started producing PFAS, someone out there was crying foul about "hey maybe we shouldn't just dump this everywhere", and they were ignored, it was dumped everywhere, and now we get to deal with the consequences because nobody listened to those people.
This has happened hundreds of times, including serious things like lead paint and leaded gasoline, which we KNEW caused direct and measurable harm to people, and yet was completely ignored. A portion of the public has obviously lost ALL trust for the private sector claiming any sort of "this couldn't possibly cause problems" and are willing and able to take action.
If you are a "big" enough entity, there is no such thing as "private". Anything you do, affects a lot of people, and you should be treated that way.
there aren’t many technical issues to pouring concrete in a good lat-lon
Other than when a powerful and explosion-prone rocket destroyed its launchpad, hurling chunks of steel-reinforced concrete thousands of feet. But it's almost 18 months since that happened.
That launch was on 20th April 2023, and the next prototype test launch was only 212 days later on 18th November 2023, although I think the pad redesign/rebuild/repair work was complete by the end of July 2023.
So only 3-4 months to redesign/rebuild/repair the pad (although it's probably reasonable to assume some design work had already occurred).
I'm no rocketry expert, but I'm old enough to remember the Space Shuttle Columbia disaster; I'm pretty sure if you've got falling chunks of steel-reinforced concrete hitting your space vehicle during launch, that's an issue.
But it was also a prototype being deliberately tested to destruction, so the context as compared to Columbia was quite different. (And it wasn't just the rocket itself that was a prototype, the pad and tower were at least a little as well).
And this has always been SpaceX's approach, rapidly iterating their design by building, testing, destroying, rinse/repeat - so it sometimes feels a little difficult to compare to a more NASA-style design process where a (usually) small number of items are produced with a significantly lower tolerance for failure.
(Edit: And how much better is it to learn these design lessons before the cargo is more fragile/delicate/squishy?)
Having chunks of the launchpad go flying isn't just an inconvenience - flying debris during launch can damage critical rocket systems, as the Space Shuttle Columbia disaster demonstrated.