His kit sounds good on paper, but you've got to compare him a bit harder to other adcs.
His damage is complete poopy. You have to accept this. His poison is poopy until late game, when it's still poopy (and by no means a tank shredder), his expunge actually doesn't do good damage at all at any point in the game (just seems strong because it's a surprise, but it does like 200 damage at level 9 after armor), and it's physical so if he doesn't get armor pen it's even more poopy, and his w does no damage. He does, however, have an ad and as steroid, giving him decent stats over other characters.
Ulting through tank to the backline may sound nice, but in reality you have to be close to their team to do that, and the backlines take massively reduced damage, to the point where it's outhealed by lifesteal. Therefore, poopy.
His ult is almost always better off used to just outrange people and flank, as you said, usually hitting 1 or 2. The reduced damage per hit makes it worthless to try and get into a risky situation to hit more than 2 people. If the ult did full damage to everyone (or old tiamat was still a thing), then he would be really good since players would go the risky path for the big bucks and try ulting the whole enemy team instead of 2 people, dealing insane damage to everyone. But it doesn't, it isn't, and so they don't. Hitting 2 people at once allows him to outdamage other ADCs, but having a vi, nocturne, long range mage, and other long range counters etc. forces him to not enter the fight until it's already been going on for a few seconds and the ultimates have been used, so his team has already been weakened by the 4v5, and by then he'll have a tough time landing it on multiple people or he'll end up using it and then run away emmediately, wasting it.
He has stealth positioning that can't easily be used as an escape, unlike every ADC and mage and tank and bruiser these days that just chase him down if they have any advantage over him or run away or dash over a wall. He can't stick to people with dashes without putting himself in danger, and he can't run. It's all-or-nothing with twitch, and people don't like risky picks.
With all that, he has his roles and picks when he's good like cc-heavy teams or teams with shen, but in general he's just unsafe and dies too easy. Other ADCs still outdamage him in 1v1 scenarios, especially early game, and they're much safer and they probably have a much, MUCH better early game, allowing them to fight whenever they want instead of waiting for "just the right moment" like Twitch.