It's difficult to find something everyone can agree on. I'd recommend making each round length in your system three minutes, like professional boxing, or even five minutes. If you want a fumble only to happen once per round, for anyone, that would also work. And it may help to roll a d6 and on a 1 the fumble happens, or even to use 3d6 in place of d20 for the attack roll because then the minimum, 3, would be more of an outlier. That could be recommended for anyone using critical hit tables, too, because of the dramatic effects involved.
I find that fumbles do bring more drama to the game. It's a balancing concept. D&D combat is abstract, and only goes so far to simulate a real combat, and it shows that even the most skilled fighters aren't in control at all times. That is how it should be, because even the Drizzt's and Hector's of the world can trip on a rock or lose their grip on their weapon. Likewise, that knight who charges in on his horse might fall off, and the fumble rules are just trying to bring those consequences to life. The idea is that the combat will only last a few rounds usually, so we will otherwise never see a fumble. It's not meant to be the norm, although it can happen a lot if the dice roll poorly for someone.
And critical hits often make a big difference even if only the base damage is doubled. The thing is, every extra point of damage can drop someone, or kill if you're playing with death at 0 hit points. Critical hits change how long a combatant can last in combat, which upset other tactics such as when to heal or retreat. They can even win a fight outright. If you use expanded rules, the damage can be much greater, and other things can happen. Instant death, or maiming aside, of course, the critical hits can sunder shields and armor, inspire dismay in foes to make them check morale, and bring you extra experience points.