The smuggler is the republic version of the operative I think
So I guess I just suck.
I know if I stick with it long enough I'll get used to it but... learning sucks!
It's not about sucking, it's like you said at the end: Learning. Most of the abilities serve as a specific tool for a character in a specific situation.
Are you playing the scoundrel or the gunslinger? Scoundrel does play like the operative and that class has one of the simplest actual DPS rotations. You'll find that as you level and apply points to a tree a lot of the damaging abilities become less important.
Looking at the Operative/Scoundrel you have Backstab, Shiv, Overload Shot, Lacerate, Acid Blade and Stim Boost as your main DPS abilities (Names are different for the scoundrel). If you never want to do anything but hit enemies you can manage with just 6 buttons plus your basic attack. Sniper/Gunslinger main dps rotation is similarly streamlined as well. You end up with two aoe abilities (A reusable one and a slight cooldown ranged one) and the rest of your abilities are situational.
I would suggest anyone unhappy with the number of abilities not to roll a Juggernaut/Guardian tank with biochem consumables.
EDIT: I will mention there are some superflous abilities. Mostly those 'incapacitated non elite enemy finishers' which are clearly just junk filler. Savage Kick also seems like a filler ability for the Warrior. For operative the 'extra stealthy stealth' ability is probably unnecessary, outside of that I use every single one of his 22 hotkeys while I'm playing and would be less effective without them.