My biggest problem with twine/HTML games actually has to do with my expectations. Anybody's who's been on tfgamessite, for example, knows that people make shitloads of Twine games all the time, and occasionally a few Twine games show up on other sites as well.
As a game engine, I think Twine (for example) is totally acceptable. I'm not the biggest fan of using my mouse for a text game rather than a keyboard, and picking out the particular colored word in a wall of text that may or may not be worth reading gets to be a bit of a chore, but I don't think it's really the gameplay that's the issue.
For me the problem is the writing, and I don't just mean grammar and spelling errors. For some reason, it seems like 50% of all twine games are about forced sexual reassignment surgery/magic/whatever and then misogyny against the guy with the mutilated genitals. Most of those games are very basic, some have a lot of complex systems, and a few are in between, but unless I know otherwise I fully expect that in any particular adult twine game at least one dude is getting his dick and balls pulped and then getting raped.
On the other hand, there are ALSO a lot of games (maybe 30-40%?) about completely normal dudes (or ladies) dating other completely normal ladies with some fairly tame exhibitionism scenes and vanilla sex scenes along the way. These don't interest me for the opposite reason, where there's no narrative tension because I don't give a shit whether the protagonist and his/her intended lady end up boinking.
As for the rest, they range from terrible to amazing. I happen to be a big fan of A Spell for All, for example, and have played a few really good HTML-based games otherwise, but in my experience to find the really good HTML games you end up wading through a LOT of garbage.