> exclusive control of supply

Is not the only, nor even the most useful, definition of a monopoly. And there's also not a magic moment where one second you're not a monopoly, and the next second you are when user X+1 signs up. It's a gradual process and that's why it is such a huge area of law.

Monopoly is semantically not very complicated. It's a fairly simple economic principle:

- Monopoly = Exclusive control of supply

- Monopsony = Exclusive control of demand

If you want to redefine it to popular things, you should reflect on your motivation to do so.

You might want to reflect on why you want anti-trust law to only apply to the strict definition of a monopoly. That's why it's called "anti-trust" not "anti-monopoly".