Thinking on specifics, there are at least a few weapon types I'd like to see that were fun and challenging in other games.
Sticky grenade launcher: No lie, this was why I liked the engineer class in FF. Screw ALL your turrets; I enjoyed lobbing grenades over long distances to blow up waves of aranhas attacking three different thumpers at once. I also enjoyed popping them mid-flight to hit fliers who thought they were safe. It was a weapon that took some timing and aim to make work, but it turned you into a versatile demolition machine.
Machine guns: I hereby forbid any game designer to make a shooter without some form of high velocity, high volume, high rate of fire weapon. I don't care if it takes both hands and prevents flight because of it's massive bulk. If there isn't a weapon that lets you hold down the button and yell into your mic while you slice the battlefield apart amid constant thunderous bullet discharge, you are doing something wrong. I am heavy weapons guy and I DEMAND MY WEAPON.
Bouncing weapons: Quite the opposite of machine guns, there are few things as intellectually satisfying as bouncing a grenade or three off a wall and killing someone you can't see behind cover. It's just such a joyful display of geometric chaos to see grenades bouncing off two surfaces like a pinball before popping in someone's face.
Blades: Shooter or no, it's hard to ignore the practicality of a sharp object that doesn't really miss. Without bladed weapons, we're bereft of the nimble melee archetype who zips in under fire and assassinates the unit leader before dashing out to safety.
Hammers: Alongside the blades, I'd love to see a blunt version that's used for smashing through defenses and splattering enemy forces in all directions. Two-handed or not, no one can deny the catharsis of a good, solid TWHACK!
Rockets: the quintessential dumbfire missile, what game would be complete without some form of long range straight line explosive? We could even have variations like a cluster bomb that can be triggered mid-air to rain down fire, or a napalm version that just burns for days. Maybe even a "riot control" rocket that deals less damage but explodes into a path-blocking foam for a short time.
As for the "elemental weapons" discussion, I think the main solution is already present: ammo types. When you give us a "cryo shotgun" you really just duplicate the "magic bow" trope--it makes the arrows magic by proxy. Yeah right. If the rounds are designed to inflame, chill, or discharge some electrical current, however...then they can be used with any weapon and are a meaningful use of resources that requires forethought. It could also be a way to throw more utility into our choices, assuming the environment calls for such functions. Are you hitting up a boreal biome? Might be good to bring some heat rounds to melt ice and hurt polar creatures more. Facing lots of automated bots? Shock rounds might be good for quasi-EMP functionality.
If the "elemental" properties are given actual purpose and physical effects rather than just a damage multiplier, then we stand to have some fascinating new gameplay emerge.
