Removing trusted phone number without adding another on Apple device

Your iPad will only become "unusable" if you sign out of it and then try to sign in again, or do anything requiring a higher level of security. I rarely see anything that requires a higher level of security unless it is doing something such as changing my password. I can go months without triggering a higher level of security prompt

My understanding is a phone number is a secondary means of sending you a verification code after a trusted device cannot be used.

For an outline, read Two-factor authentication for Apple Account - Apple Support

You will need a phone number:

About trusted phone numbers and trusted devices for Apple Account - Apple Support

"To use two-factor authentication, you need at least one trusted phone number on file where you can receive verification codes."

Ask a friend or relative if you can use theirs, or get a cheap phone service. I pay $7/month for my no-contract service. If you have another Apple device that can receive a code you should only need a number once when you enter it and receive a code that way. Otherwise a Mac computer or whatever can substitute.