Here are a few alternatives to a cell phone number that could be used to start an account.
1) Paypal account.
You will need it to be paid anyway, so this is ideal.
2) Facebook account.
Facebook only allows one account per person, too!
3) Bank account
This should be deleted after usage with only the last four digits and bank name kept in the system for safety reasons. This is enough to prevent multiple accounts while respecting privacy.
These suggestions are here because I know many people who own multiple cellphones. Cellphones are not a good indicator because of that. It also allows people who aren't in the US to join.
It would also help if in your TOS it said more of what you do with the cellphone number and/or promised that the number is NOT going to be given to advertisers. Explicitly stating that the number is going to be deleted from your system (or at least all but the last 4 numbers and zip code) after sign-up is done would be nice.
People have learned not to trust advertisers with their cell phones and no amount of praise for the company in question will fix it. Only transparency about what is done with the number and assurance in the TOS that if it isn't used for more than signing-up it is deleted/altered from the system so it can't be used will help.
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