Shredder Ammo is left behind, and some of that has to do with the damage, but it is also due to the fact that it doesn't offer any CC whatsoever. Warp and AP also share this limitation, but at least they can damage certain defenses.
Since ammo damage in ME2 is calculated from the base weapon damage, the actual percentage of your total damage that ammos do will decline as you level up your guns, and especially when you research higher multipliers to protections.
If I was stuck with Shredder (say I took it as a bonus on a Soldier for no good reason and was dead set on running it), I would probably always run with Miranda and Garrus and have them strip protections for me. I haven't ever done this, although I have done AP ammo soldiers.

As for Thane, Warp is nice against armor and barriers, and for warp bombs, so he is best paired with a biotic Shepard and / or used on missions against the Collectors and the Blood Pack. He isn't quite as good on husk horde missions unless Shepard has a group armor stripping ability, or you pair him with Mordin, which will allow you to use Throw Field to rapidly clear groups of husks. He is next best against Eclipse since they have a decent amount of units with barriers and armor, and he isn't quite as good against Blue Suns and Geth. Of course this is all relative, and whether or not he will work out against a specific faction depends on what role you assign him in the squad, who the other squad mate is, and what class Shepard is. Overall I would say he is fairly versatile, clearly not as specialized as Tali or Legion, but also not quite the jack of all trades that Miranda is.
cap and gown wrote...
The only reason Thane would be running into bullets is because you are not taking point. My standard practice is to run into a room, pause and look for cover, put the squad in cover and then push forward so Shepard has point.
Basically this. Essentially the enemy AI in ME2 will prioritize the closest target, so it is helpful if you place the squad in cover somewhere behind where you take cover as Shepard. Most everyone on the team does not tank all that well on the higher difficulties, especially left to their own devices.