Is there anything that prevents a governmental entity from passing any regulation that requires or prohibits an action and then claims a right to randomly inspect (aka search) to enforce compliance?

Yes. Politics.

Most of the protections of the U.S. Constitution, and especially state constitutions, are procedural. The genius of those documents is not that legislative or regulatory power is denied to the government. The state legislative power covers everything, for the most part - only the federal government is limited. But the exercise of that power is allocated in ways that mitigate against the chance that the government will do something that its citizens really, really hate.

That's not perfect, of course. Especially when it comes to actions taken by the majority against the minority. Which is why there are some broad areas that are indeed walled off from government action.

But for the most part, the protection against government doing things like you describe is the ballot box.