If someone invented time travel and used it in a tourism business, would government leave it alone?

Slightly different from what you are asking but there is a great novel about a government sponsored time travel project. It is the 1970s cult classic Time and Again by Jack Finney. It does delve into ethical questions but not in the public vs private way you are speculating about.

^^Thank you! Would love to read that. Lost my interest in fictional time travel stories and now it’s back.

No, and they should not leave it alone.

It’s one of my all time favorite books.

^^Last one I read years ago ( can’t recall the title right now ) was about one guy’s trip back to 1800s NYC, imbibing the culture and eventually falling in love.

Oh wait, just googled it and it’s also by Finney! It’s the sequel “From Time to Time.” Lol

Of course they wouldn’t the Government has to stick their nose into everything.
At first they would claim it’s a safety issue, but then they would see how they could use it to their advantage then how much tax they can get from it.

Robert Silver erg covered a bit of this in his 1969 novel Up The Line. It’s pretty lightweight, but a fun read.
https://www.barnesandnoble.com/s/Up+the+line+silverberg?_requestid=4281520

Hell, no! Taxes are taxes, or as the 110th Ferengi Rule of Acquisition states, “Exploitation begins at home.”

Nope.

Not on your Nellie!