I really don't like having to defend a shitty company like Gearbox but some of the stuff you posted is just wrong
You can see Lasers (from tps) and what looks like grenade launchers in the trailer, I can understand how you'd miss it since it's really fucking hard to see what's going on because the mongoloid who edited the video decided to show the gameplay in millisecond-long clips
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That's really only a thing in Borderlands 1, in BL2 with the exception of Zer0 the rest of the characters have no more one skill and/or class mod that gives them a boost to a specific weapon, and have viable builds that make use of most weapon types. And since you used the soldier and the Siren as examples: Axton has one (almost completely useless) Assault Rifle skill and one (even more useless) class mod that boosts ARs, Maya has one (really good) class mod that boosts SMGs and no skills at all. There's really no reason to restrict yourself to one or two weapon types unless you choose to build your character that way.
In the end you are right with most weapons not being worth using but it has more to do with the fact that certain Manufacturers+Weapon Type combinations are better than everything else, but isn't that the case in every loot-focused game?