I use them all the time with Fender single coils (strat, tele, jazzmaster).
On humbuckers and P90s, not really very often at all - I leave them fully open. I sometimes think I can do without, but very rarely it comes in useful.
If you unsolder the tone pots and remove them you should notice a slightly brighter tone.
same here. other thing is, as you said, because removing the tone pot makes things slightly brighter, if you have a tone knob you might always leave it on 10, but things might be too bright with it removed.
That is true - things might be too bright with the tone pot removed (generally I like to have things bright, so didn't consider this a negative).
One thing you can do, is wire the tone pot so its permanently on maximum. To do this, remove the wire (or it can be a capacitor with long wires) which is connected to the middle terminal of the tone pot. Solder it instead to the terminal which is not connected to ground. Then the tone of the guitar will remain just the same, but adjusting the pot will no longer have any effect.
Kiichi has already mentioned 50s wiring, which is another way of wiring the tone pot, but it gives you a more effective range of adjustment and a volume control which is less muddy. Lots about that online. Search 50s wiring, or modern vs vintage wiring.