Yeah, but the only real problem we had there was Jack (needed Barrier or Reave), and Jacob pre Barrier. Even Tali isn't really that sqishy. Like other Engineers, she has large shield pools, shield drain or damage reduction powers in all games. Most other shotty squaddies were practically tank characters.
Tons of shotties were great mid or even long rang weapons, though. Claymore, GPS, Wraith, Graal, Crusader, or literally any ME1 shotgun around midgame on a character with training. In ME3 they were unquestionably the best overall class of weapons for general purpose use, in large part due to high damage in both burst and DPS, as well as the probably overpowered smart choke mod (and other accuracy boosts like Marksman or Hunter Mode) giving them a little too much range if anything.
I don't get these complaints, anyway. My squaddies rarely ever get dropped. They aren't very smart, but if you build, position and use their powers correctly instead of letting them derp about Overloading armor or Warping shields, there are few issues.
The Jack design was really dumb. Not only did it not show in game even a fraction of her supposed biotic power, the power combination was useless to the point of me more or less ignoring her on missions.
The problem with shotguns was mainly during ME2, and yes, Tali had trouble on her loyalty mission - thinking back, this one might have been actually easier due to relatively close quarters, but in open spaces she certainly struggled every time because of this weapon choice.
Is she better than Jack? Maybe, I didn't take either of them most of the time. (Tali at least had some mildly useful powers, so I may have used her a little more)
Also you are confusing between MP and SP. There is no Hunter Mode in SP, I never really played the soldier class on SP anyway, and Marksman power is only accessible to Ashley in ME3 IIRC.
Squadmates are generally equipped with a rather dumb AI, give a weapon that loses effectiveness at range, and they are even less useful.
But why should squadmates be restricted to certain weapons anyway?
Luckily I play on PC, I hacked the game in the past to give some of them different weapons than their default ones.
I mean, why can't Miranda use an assault rifle? It's actually somewhat easier to master than a pistol in RL...