One major downside to this.
If you loose your phone, drop it down the loo, brick it, loose all the data on a software update etc etc you have to prove your identity via customer services to get it removed from account.
This is a long winded process that involved sending off something along the lines of a drivers licence or passport with other games, not 100% on Bioware/EA policy but I'd be surprised if it were much different.
My authenticator is next to my PC, if I had a laptop it would be tied to the laptop in some way