i hope its an intented mechanic bc its anti weaving and makes fights more interesting, on abrams u just have to wait a little longer before dashing so a timing u have to master. meleeing thing is like how meleeing also pauses reloading (also another anti weaving), heavy melee doesnt pause reloading instantly so thats the same reason(or simular i believe) u only notice it at point blank range on silver bc u can still reload or still complete the bullet cycle in the time between the heavy melee. reason i said believe is bc im certain long ago heavy melee only stopped reload after u hit something (bc i did it alot against mid boss) and that bullet cycle followed the same rule and they might have only nerfed the heavy melee reload but not the bullet cycle so thats why its only at point blank and not at farther range also but im not certain.
After having some time to sit on it I'm on the side of the mechanic staying in the game. There definitely is room for some sort of feature or rework to have better feedback for when the cooldown applies versus when it's timed successfully to avoid the cooldown. Or somehow change the mechanics to feel more consistent and so it doesn't feel accidental when it sometimes works or sometimes doesn't.
The reload pause makes a lot of sense when it gets paused by dashing and melees because it makes reloading a more deliberate process when meleeing and dashing can be performed while reloading but at the cost of delaying reload. So while reloading, melees and dashes can't be spammed for free movement or damage and the cost versus payoff of doing those things is always an important consideration. It does limit the fun, but for the same reason hmc's had to be removed, if that system wasn't in place spamming dashes and punches would be the optimal strategy and there would be no room for other movement options to have their place in the game.
One thing I thought of just now is how crucial it is for low fire rate heroes to have a longer and more punishing cooldown from a balance standpoint. Low fire rate heroes, whether they have a shotgun or an alt-fire mode, tend to have guns that perform best in close quarters whereas high fire rate guns sometimes are even worse at short range because it's difficult to consistently track someone when they move so quickly close up on the screen. If low fire rate heroes had the same firing cooldown as high fire rate heroes, it'd make close quarters fights even more favoured towards low fire rate heroes because they will be able to dash and melee for free in between their shots on top of their designs innately doing more damage in close range.
There's probably many more reasons why this firing cooldown is healthy for the balance of the game, but I still believe that learning how to work with the system and feel tangible feedback for when and how the system works could be super helpful.
One thing that I find has similarity to the firing cooldown is L-cancelling in Smash Bros Melee. There's a similar situation in that game where jumping and landing on the ground normally has a really short landing animation, and if you perform an aerial attack and it doesn't end before reaching the ground it will have a certain amount of landing lag depending on how "powerful" the move is. But by pressing 'L' in a few frame window before touching the ground, the landing lag will be halved allowing for characters with otherwise slow and laggy moves to level the playing field with other characters with naturally fast kits (who still benefit greatly and lose nothing from L-cancelling too). There's some discourse about whether L-cancelling should even be a mechanic or why the game doesn't automatically give everyone L-cancels, but the mechanic fits well in the game in that learning to do the input and mastering it will be intuitive to someone with good knowledge of their character's movement and moveset. It's both a good balancing mechanic that allows slow characters to stay viable and a technical mechanic that not only feels good to pull off but will reward players for having a good mastery of their character.
I wrote a shit ton up here jeez. Anyways, in essence you're right that this system benefits the game in a lot of ways. Also I don't know if there's some analogue to L-cancelling in other fighting games or games in general but there's a lot of potential there and possibly a way to use those systems as inspiration to make the firing cooldown feel more consistent and satisfying to use.