Privacy flaw and a security flaw: it is feasible to take over somebody's phone number through social engineering attack on the phone co's tech support. The tech support has ability to issue replacement SIM cards for users, and if an attacker socially engineers them to send SIM card with your number to them, it's a game over for you.

That is aside of the obvious problem of phone numbers being recycled for re-issue after having been abandoned for a stretch of time.