it's suzy

I would play the fuck out of that game if it existed

not quite the same, but you just reminded me of Mega Man 8, where every weapon's cooldown is independent of each other, and switching is instant. In speedruns and especially TASes, they can switch back and forth between 2 or 3 weapons to fire all of them each at full speed!

Haven't played it but it seems that DOOM Eternal tried this, and I also saw people finding it either obnoxious or unclear when it came to deal with enemies that forced you to switch up weapons.

It also became a speedrunning exploit against those types of enemies as well: https://youtu.be/1EmAQ1BdRAk?t=4447 (DLC end boss spoilers btw!)

Definitely a delicate balance to be struck.

Battlefield Bad Company 2 had a thing where you could cancel reload animations by switching weapons. If you did this after the mag was in, but before whatever else unnecessary thing, the game considered that enough.

I often think of ZPC, which has only one gun, the "Jerry-7", which has several modes of fire, including a pistol whip. Like everything else in ZPC, it's the hint of a fun idea that is boring in execution.
🤔 It might be fun if your character has two hands, each with its own gun, so you could use either at a moment's notice without switching. There's an obscure SNES game, "Phantom 2040", where you equip two guns at once ... and each has a unique combination effect. Power-stancing guns, imagine.

The closest I can think of is Ultrakill, but nothing in that game I'm aware of is based on landing attacks