I think that is reasonable in principle. Thinking further, enforcement—not just regarding mapping multiple buttons, but in general—might be another can of worms... Consider these different ways, of varying legality, to shoot quickly:
-using multiple default shooting keys (left shift, space, right shift) -using multiple remapped shooting keys (e.g. j, k, l) -very fast mashing or piano-ing two or more fingers on one shooting key or button -mapping multiple shooting buttons -using a controller and keyboard simultaneously -a non-blatant turbo macro -miscellaneous goofy setups (mouse wheel mapped to shoot, foot pedals, etc.)
I don't think I could distinguish between these in a recorded run, even with inputs displayed.
Using this technique, you can get higher DPS with weapons that seem to have a skippable shot delay (Machine Gun, Triple, Noppy, Burst and especially Puncher). You also get a slight benefit with Laser and Shotgun, since although you need to wait for their delay before firing again, more presses as the delay ends means a potentially-earlier next shot.
Also, using this technique when your gunboots are empty actually gives you a decent 'brake' (since shooting while empty reduces your fall speed just a bit). Not sure how useful this would be for the run, but just something I noticed.
Since it's in the game, I also feel it's probably fine. Though as a controller player, it makes me wonder, should mapping multiple buttons to shoot also be allowed, for parity? (I think I just have one button for shooting—I don't know if that's something inherent to the game or just the default mapping Steam gave me.)