Linking an account to a phone number

Yes, it would be possible, with some considerable costs (considering that a customized solution is needed) - and it will take effect ... at best a few weeks.
Other much bigger games have already implemented this system for sometime ( you can search them over internet ): phone number + hardware ID + many other details, so that you can no longer create a new account if you have been banned ... and everything went very well for about a week, after which the cheaters found solutions to bypass all these restrictions and can create new accounts after being banned - in other words the costs of implementing such a solution do not justify themselves because they are not reliable.