I don't see how people could have the time to browse the internet in the middle of a fight. I've played through the game and didn't experience long waiting times at all.
Sounds like impatience (or ADHD) to me. :S
Maybe you're just a slowpoke. xD
Anyway, waiting 30 to 60 seconds for a group of enemies to end their turns and the 2-3 second pause between casting spells/skills is annoying IMO.
I don't think the combat is boring, I really like it. It is just rather slow in D:OS and should be speeded up.