I have seen many implementations of crit fumble rules. They all resulted in slapstick combats where fighters came out looking like idiots. (And, as others have noted, multiple attacks make high-level fighters look dumber than low-level ones.) Hard pass from me.
As for critical hits, I think a crit should be guaranteed to be the highest damage you can do. To achieve this without changing 5E's combat math, have crits deal "max plus one" on each die; so if you're attacking with a scimitar for 1d6+5, a crit deals 12 damage, as if you had somehow managed to roll a 7 on that d6.
"Max damage" is simpler but depowers crits a bit relative to the 5E baseline; "max damage and roll again" is a bit more complex but also more impactful; both would also work fine IMO.