I can play Priest (all 3 specs), Resto Druid, Mage (all 3 specs), Ele/Resto Shaman, Prot Paladin, and BM Monk each probably 90%+ optimal. I also mained a warrior for 4+ years so I could probably re-pick that up fairly quickly.
Honestly, all it takes is 20 or so minutes browsing forums/logs/armories, 20 minutes setting up an optimal UI, and an hour or so practicing in LFR. I'm also a raid leader which requires me to know mechanics from the perspective of all roles, so picking up new things in different roles isn't an issue for me.
This is all PvE wise of course. It takes longer to master a class in PvP. I've played my Mage, Priest, and Warrior to 1800+ levels, though I've never been a serious PvPer.