what I (see name below) dislike the most

My worst shard task force only took a year and a half.

Honestly, I don't think I could tell you what any of the TFs are about, even though I've done all of them multiple times.

Speaking of the Council, every time I run the ITF I'm curious why Nazis are building a giant robot in Ancient Somewhere In The Eastern Med. But never enough to actually make the effort to find out.

I remember an old-style Posi where everyone in the team was level 10 to start. We slogged through the first map boss by purple-conning boss, teamwipe by teamwipe. Slowly, people dinged, and the fights got slightly easier. The whole TF took hours, but no one ever even talked about quitting, and overall it was really good fun, in a slightly hysterical, masochistic way.

I think that's a problem inherent to the contact-mission setup as a whole, not to the TFs themselves. Aside from a few easy-to-miss speech bubbles inside the missions, all the information is conveyed via talking to the contact. Which only the team leader interacts with. And because they don't want to keep the team waiting while they read, most people skip past it as a courtesy to the rest of the group. Unless you're a roleplayer doing the entire TF in-character with other roleplayers, most of the TF's plot and setup simply aren't made available to most of the team.

More recently-introduced TFs like the revamped Positron and Penny help that a little with the introduction of the cutscenes that everyone gets to see. Even so, you spend most of the TF running around just doing what you're told by the game, then a cutscene comes up explaining that (*SPOILERS*) the city councilman you just rescued orchestrated a supervillain's escape from prison so she'd destroy Terra Volta and he could build a new, more efficient power plant in its place, but she threw him a curveball by getting her hands on a Council device that threatens the entire city and now she has to be stopped. And suddenly you're like, "oh, so that's what we've been doing for the last three-and-a-half missions."