OK - longer posting again 
It would have been a definite plus if each mission had brought something to help you in the end or taught you something relevant to the general plot like they did with Tuchanka in ME3.
I agree, but I think this is a VERY hard goal to accomplish if you want that for all companion questlines. For me it is enough if the personal story teaches me something relevant about the character and I think it is a nice bonus if it teaches me something about the world and the race(s). And I think most companion missions in ME2 did this.
Jack -> Learning about cerberus.
Jacob -> Learning about colonization dangers
Samara -> Learning about Asari mythology
Tali -> Learning about Quarians (and also Geth) life and history
Legion -> Learning about Geth (and also Quarian) life an history
Kasumi -> Learning about criminal power in the citadel sector
Garrus -> Learning about criminal power and lifestyle in terminus systems
Mordin -> Learning about Salarians, Krogans and Genophage
Grunt -> Learning about Krogans
Thane -> Learning about Drell and Hanar
Zaeed - Learning about Blue Suns
Miranda -> Learning... only about her family and a little bit about Cerberus.
What I can imagine for nextME: Companions that will be met in new locations and that are linked to that locations and you have to help them somehow to recruit them. Companions you meet somewhere else, but who have to "solve" something at a special location. Companions who know somebody important at a special location which is the entry to that important personality and by getting know this special relationship between "location-vip" and companion you learn a lot about the location.
And also I can imagine not only to have one quest, but a questline of several quests.
It also would be nice if this things "develop". Like the companions quest line of the first star wars trilogy
- yes... Han Solos personal issue with Jabba is in my opinion exactly that kind of side-quest I like to see. It has absolutely nothing to do with the "big war" - but its a great bonus for the movies, like the whole character of Han Solo is a great enhancement of the trilogy.
And of cours I would like to see daddies, mothers, daughters, sons, uncles, ex-partners, etc etc... of my companions and offer me a nice bunch of relationships, intrigues and conflicts. Personal conflicts are for me much more interesting than just a war like any other.
By the way - yes - all this dont need to be "mandatory". I dont care if Bioware even puts a non-story-mode in the game, that lets you shoot without talking. But if I dont get emotional stuff, especially of my companions... I dont see the point, why nextME should be something special. That would be just another scifi-shooter I would buy a few years later as 5-euro-game-of-the-year-edition. But... if this should be the way of ME... I would accept it. Would leave more money in my bag for other stuff 