The biggest problem with this idea is that not everyone has a usuable phone. Especially those under the age of 18.
Blizzard’s Phone Verification tool does not allow VoIP numbers to work.
To clarify, it is not a violation for players to have more than one account. If a player is deliberately throwing, report them for gameplay sabotage. Don’t worry about those who may be boosting as Blizzard has internal systems which track this behavior. (Click here)