But if you are attacking more often, you have more chances to fumble, so of course it might happen more because you are risking more. Every time someone swings a weapon, there is always a chance it might get stuck in something on a miss, or slip from their grip, etc.
Sure, that's "reality." Doesn't change the fact that's it's annoying that the class with the schtick "good at fighting" gets penalized more.
No where does it say a Fighter with 3+ attacks must take all the attacks. If they want to be "cautious", they certainly can, and risk less fumbles. etc.
If you have to be cautious with your main schtick because of harsh fumble rules - but other classes don't have to be careful with theirs?
Are you also imposing a spell mishap table? It's only fair.
I tend to prefer fun, cinematic combat in my D&D games. Plenty of other systems for the grimmer grittier styles.
Also, unless you have a TWF, this isn't happening until tier 3 and higher, with the rare exception of Action Surge being used.etc.
Action surge is a short rest ability and happens all the time. even without it, with haste and the like fighters routinely get 3+ attacks by tier 2. Monks can get 3 attacks by level 2.
If you are really concerned about it, you can always say Fighters have advantage on checks to avoid fumbles. Problem solved (again, using a confirmation roll system).
Or, I can just not use critical fumbles.