"Stealth has to be delayed when taking damage, except for certain ultis( KhaZix for example)"
Says who? Akali's shroud doesn't care about whether or not she's taking damage. Wukong's Decoy doesn't. Teemo's passive doesn't. No stealth ultimates except Rengar's care.
Srsly, why is he not being played more?
He's mediocre unless you're really, really good with him, and even then he's not better than any other champion with a similarly skilled player is. He can work ok in solo queue, but he's very easy to respond to in competitive play. There is a large risk of falling off hard and becoming very weak as the game goes on. He may deserve a bit more play than he gets, but not much.
Vi, Lee and J4 being out of the meta doesn't really mean anything for him. Lee may be a bit hard, but Vi and J4 are pretty neutral matchups. I'd actually give Shaco a small advantage in those matchups. Certainly nothing special. However, champions like Nunu and Rek'sai are pretty miserable for Shaco to face, and damaging tanks like Sejuani can roll him hard if he doesn't beat them very hard early on, so he's not really doing great when they are prominent junglers.