You're completely right, and that's actually kind of my point: all in all, Twitch is not a DoT champion right now, because his DoT has very little time to act during his typical kill window, the latter of which is closer to that of an assassin. If he were focused on his DoT, it wouldn't be too bad, because that would at least force him to kill his targets over 6 seconds, but right now he's this bursty champion built upon a kit whose core mechanics don't really lend themselves to burst.
One of the issue I take with many old-style AD carries, Twitch included, is that often their kits feel like empty vessels to be filled with lots of powerful items. His stealth is rather good, but otherwise his W feels weak, his E is boring, and the rest is just steroids and an innate that becomes practically invisible when he starts getting his core items. Even his AoE attacks on ult, which used to make him unique, are achievable now to a lesser extent with any marksman who buys Runaan's. There is effectively very little to Twitch that makes him truly unique at this point, and because of this I think he needs adjustments that remove as many of his generic steroids as possible, in favor of legitimately thematic and interactive effects.
Contagion is a theme many players bring up with Twitch, and I think it would be cool to have him play around spreading his poison and exploiting it, kind of like Stukov from HotS if he were damage-focused. I think making Twitch an assassin was a mistake, and I feel it would be fine to give him good repositioning via stealth without having to give him burst on top of that. At this point we really don't need marksmen to have reliable steroids, especially not pure stat steroids, and so giving him power that his opponents can actually outplay would allow him to feel a lot fairer when he's strong.
