Uh, no, there are like 3 sets that have shorter recharge for tier 1/2, and 16 seconds for targeted AOE is very normal, few exceptions. Can you highlight some sets besides fire that are faster?
e: in any case rad/rad is a very good combo, -def is a useful secondary effect and you can put Achilles' Heel proc pieces on most of stuff if you like. My own rad/atomic blaster is one of most satisfying characters to play, good luck