I think max endless is not the best example of Minigun weakness as at the end of the day, Microguns exist and do the bulk of the damage there anyway.
However, in leaderboards for Normal mode, aka max Normal research, Minigun is best performing not even at the highest upgrade levels, but as a low level Vulnerability debuff stick. Upgrading Minigun is not only more expensive, but is also detrimental for such a use, and the DPS Minigun dream is not viable at all at high research.
With that said, at No Research, Minigun is one of the strongest towers, clearly showing that the main issue lies in how research affects the tower.
My proposed solution is adding a DeltaPower of 1.35 or higher in value to the Magazine Capacity. This would allow Minigun to scale into max Normal and Max Endless, while preserving its No Research strengths and not breaking it.
The alternative solution is a Reload Speed research.

One thing I think of is in all existing and depicted sentry guns or miniguns, there is not a single one which spend more time reloading that actually firing, even at max rate.

I know the game is by no mean accurate or realistic, still, making such an useless tower is ridiculous. And by the way ZiHell, microguns unfortunately don't spawn like hell (no pun intended :) ) but are very limited in number and so don't do much damage all together. Watch the video, there are just half a dozen at best despite many avail platforms.

I believe the tower should have some parameters to make sure it spend more time firing than reloading, by a way or another, like reducing fire rate and increasing magazine's size.

I don't understand why you had to mention the microgun count cap like it contradicts any of my points. At max Endless, Microguns do a combined total of 474% DPS of the main Minigun, never reload, but don't provide debuffs. This means the main Minigun is mostly unimportant, especially if you get a Chain Reaction (Ultimate) Venom to spread the debuffs from Minigun for it.
Balance in max Endless mode is almost never a priority over max Normal or no/low Research, so any proposed scenario should not only aim to improve those first, but also ensure it doesn't break the balance there. With that in mind, lets see the options for the fix:

• anything involving reducing effectiveness on minimum level - impossible midseason
• convert a part of attack speed into damage on higher upgrade levels - better, but still a bit scary midseason
• increase base mag count - breaks NR, doesn't improve anything
• increase flat scaling on mags - hard to make meaningful for Normal, doesn't do anything on Endless, still scary for no/low Research
• parabolic/exponential mag scaling - as I have suggested, has fairly desireable effects on all 3
• attack speed scaling on mags - i don't quite envision how this would work to comment on it
• shooting time stat to replace shooting amount - another neat option, desireable for all 3 research states, but takes more dev time.
• reload speed GV and research - unsatisfactory solution on its own, but a working one

Moving to the ideas category since it is not clear whether this change improves the balance / is safe to be called a pure mid-season buff or not