It's a lot easier to add the rest of the solar system if it rotates around the Earth horizontally, and you need that to explain the day/night cycle, seasons and tides.

Call me weird if you must, but I would prefer a globe rotate in the same fashion as the planet does: around the poles.

That's perfectly compatible with the poles being on the sides and the equator being on a vertical plane. In fact, many globes can be tilted to this position and the main rotation still happens around the poles.

Granted, but surely that would place "all points" on the equator "on top" rather than "some point"?

You're right, I spoke imprecisely. Some point on top to begin with, any other equatorial point you want with a quick spin.

They all do, but you can have more than one dimension of rotation.

Look at https://www.amazon.com/dp/B085K2ZPWB/ .

You're still free to spin the earth backwards, though.

Interesting, so a globe on a 90 degree axial tilt rather than a 23 degree one. I'm sure I've seen such (either fixed at 90 degees or variable from 0-90 degrees), but I can't see any after a quick browser online.