Billionaires still need the protection of a nation state. Their wealth would go away quickly if they had to finance an army. Maybe trillionaires can pull that off.

He'd have to have them on bitcoin payroll.

Maybe some kind of cryptocurrency, but it's unlike to be Bitcoin. When people get paid, they want the value of their payment to not massively go up/down each week.

You can be paid usd amount at the fx at the time of transfer in bitcoin and you can convert it right away if you want. Or use stablecoin for transfers. It's actually relatively trivial to have dozens of options of payment options depending on employee preference (I mean once you have cryptocurrency payroll setup it's not difficult to have all available options... available and customizable by receiver).

How far are we really from private armies really? Sometimes I feel like the US is descending back to feudalism. The billionaire tycoons of today are just lacking homage of some PMCs to be modern day barons of their own domain.

The "army" for these billionaires is an army of lawyers and lobbyists.

... then again that reinforces the existing system, not a descent to feudalism.