Yeah, that back up and shoot (or in a best case scenario, circle-strafing) is one of those problems that seems to plague FPS's, mine included. Doom 2016 famously managed to solve it with their "get in close and quick for extra bonuses" system, I considered something like that, with having the Gears blink out and then disappear, but I didn't like it at all, it just felt unnecessarily punishing. I do think if there were enemies shooting back at you, you would be forced into cover a bit more, which adds dynamism, that's an obvious add. What do you think? I would love to hear your thoughts on how you think the strategic depth could be improved-- what weapon or system designs might encourage more forward/aggressive play?
I think the two major ways I'd approach it is through:
1) Changing up the weapons so their projectiles travel differently. Maybe change the lazer into a flamethrower that is close range, but hits a bunch of enemies at once. Or maybe have one gun that is objectively the best, but has almost no ammo. Things like that can change things up a lot. Other than that-
2) I think you were spot on about varying the challenges enemies provide. I'd design weapons that you actively think are fun and with great feedback, and then make enemies while thinking how they'd interact with each weapon type. In the flamethrower example, you can have a swarming enemy with a ton of low health weapons the flamethrower hard counters.
Anyways, I don't play a lot of shooters, so my ideas are probably not the best, but that's the best I got as far as ideas go!