it is mandatory these days to submit your phone number to exchanges to continue using them especially binance. there is no escaping from authorities even if you have those fresh wallet all the time. in your suggestion, going places all the time just to login will be hard to do.
point is.. you can register a number. and use it once..
.. its only mandatory to use the phone everytime for sms if you enable the 2FA meaning you end up having to move around to hide home location if you use 2FA
ive done it myself.. bought a simcard used it to register. and then took out the sim card and never used it again. because i dont use sms 2FA. thus i dont need to move location per use to obfuscate my home location
for me the better security is to not use an exchange as a custodian. if you never leave funds on an exchange. there is nothing to steal