Would you like the squadmate to make a comment when chosen for a mission?

I like that. The comments by squadmates when picking a fireteam leader was nice and depending on who is recruited, different comments are heard

Ha. That would be alright.

I would add another trophy to match that.

Here. Have a drink - When a squadmate whines, Ryder can give a baby bottle  to the squadmate if the right dialogue is chosen.  excellent

Playing ME2 at the time of posting. Zaeed, Tali and Thane immediately come to mind, outside of missions they're required for.

There are missions that I've never taken squadmates on, but overall, I can't say never especially in ME2 since squadmates were required for their loyalty mission.

I do have a least used squadmate list. It would be Tali, Jacob, edibot, Liara, Garrus, Legion, Thane, Kasumi, Grunt, Wrex, Garrus, Samara, Jack, Mordin

That would only be most of them, particularly in 2 and 3.

ME1- Usually took whoever I was romancing at the time, and Wrex or Garrus. Often Liara and Ashley regardless. Kaidan especially, gathered dust until reduced to dust.
ME2- Miranda and Kasumi except for loyalty missions or certain special situations (like taking Legion to the Migrant Fleet). If squadmates had or should have, interesting dialogue related to a mission, I'd take them. Or if I had multiple missions on one planet. Tuchanka for example has always been Grunt and Mordin for both. They both have business there, one less shuttle trip to get everything done.
ME3- Javik and EDI usually. Sometimes Liara.

Otherwise to the OP, that video reminds me of Diablo II's character select. And yes, I would be down for generic comments for selection/deselection. Though maybe not with such extreme reactions on deselections. I was expecting the equivalent of "aww, damn" not "son of a bitch!"