if everything is solely free market so is law enforcement.

Yes exactly.

Billionaires could just buy being right even more than they can now.

You think a billionaire can buy every law enforcement agency that exists including all future agencies that exist in perpetuity?

All this without ever making a profit?

That's literally impossible. Money runs out if nobody is buying your shit and if you keep spending it.

Do you think you can become a billionaire without offering things to people that they want to willingly buy?

"law" becomes irrelevant if I can pay more people to enfore my laws than you can to enforce yours

See the above comment.

Unlike the Government -- you do not have a monopoly on money.

Therefore you cannot print endless amounts of money to enfoece your attempted monopoly on Law and its enforcement (which is what the Government does now).

That is not sustainable -- you will run out of money.

The "what if" scenario you are describing is literally the Government now as ir exists.

The nightmare scenario you are creating is the one we already live under.