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but surely it can't draw more power than is available?
The amount of power available is going to be designed to be split between all the ports and other 5V devices in the computer. That could easily be enough to damage the port or the circuit board if it's all drawn from a single port.
Whether that's actually possible depends on how proactive the circuitry is about preventing overloads. If the chosen method is just pop up a dialog while continuing to supply power, that's not good. Hopefully there's something to actually cut it off eventually.
OTOH electric motors draw a surge of current when first switched on, which might be enough to pop up the dialog without continuing long enough to damage anything.
If you're concerned, get a USB "charger doctor" to see how much current it's actually drawing when running.
I got a fan off ebay and when I plug it into my laptop it says;
There's lots of stuff on the internet about how to fix this pop up. But my question is does it matter? The fan spins.
It's pretty obvious that it's the fan causing the pop up, but surely it can't draw more power than is available?