The general idea is good in the sense that it would probably help reduce cheating. How ever implementing such an idea is the hard part. Phone numbers can be spoofed. Phone numbers are also recycled. So you would run into the issue of people having their personal numbers spoofed and banned for no reason.
If they wanted a reliable system like what you suggest I suppose it could be done. How ever doing so would be difficult and expensive. The labor involved with verifying accounts/people would be huge. They would need someone to manually review every application and approve or deny it. That's a TON of labor to pay for especially for a game that many play for free (or close to it). It also would turn a lot of casual gamers away from the game. Doing something like what you suggest would probably require copies of Government ID and other things to verify identity. That will turn a ton of gamers away, including kids.
Personally I don't like handing out personal information. If a gaming company was asking for that kind information up front just so I could play. I probably would just find a different game.
EA and the gaming community (us) would be better served if they just continue to work on their anticheat system and an AI system that reliably deals with cheating. It's just cheaper, more effective and less confrontational with the consumer.
