I actually loathe such rules because they punish Fighters and Monks.
If I were ever to make such a rule for 'fumbles' it would read:
'If your first d20 roll on a turn is a natural 1 then the result is a fumble, and... [bad thing happens]. You cant fumble more than once per turn, and you can only fumble the first attack roll, saving throw or ability check you make during that turn.'
That way Fighters and Monks dont get clumsier as they advance in level.
One of the heartbreaker mechanics I've played with is that extra attack goes away.
Instead you start getting combat expertise, which gives you advantage-like d20 mechanics and extra [W] damage.
Heartbreaker Fighter (10 levels).
Expertise: Fighters are experts at combat. When making an attack, they roll 2d20 and take the better roll.
Weapon Master: Starting at 2nd level, a Fighter gains additional weapon damage dice equal to half of their Fighter level (rounded down). When they make an attack, they can distribute them over creatures they melee, using the same attack roll for all of them. Add your strength bonus and "on hit" effects of the weapon once per target, not once per die.
Athlete: Starting at 3rd level, the Fighter's training of their body has resulted in remarkable results. Increase the Fighter's Strength, Dexterity and Constitution scores by 2, and another 2 points at 10th level (max 20). If this would cause an ability to pass 20, the remining points can be assigned to a mental ability score (max 2 per score). In addition, the Fighter rolls 2d20 on all physical ability checks and saving throws and takes the better result; at level 10 this extends to all saving throws.
Champion: Starting at 5rd level, the Fighter is a champion who can inspire others to great deeds. The Fighter's loyal allies add 1d4 to their attack rolls, saving throws and skill checks while in the Fighter's presence or following her plans. At 9th level this increase to 1d6.
Loyal Allies: A creature is a loyal ally if the Fighter's accepts their allegiance, they respect the Fighter, follow her suggestions, and will not or cannot work against the Fighter's best interests. Fearful underlings can qualify as loyal allies. If the erstwhile ally betrays the Fighter, they lose this bonus.
Protector: At 7th level, once per round the Fighter can move her speed and protect a creature they move adjacent to. A spell, effect or attack on the creature is blocked by the fighter (possibly pushing the ally out of the way) if physically possible, with the ability redirected to the Fighter; any to-hit rolls or saves must be repeated on the Fighter.
A level 11 5e fighter with a greatsword and 20 strength deals 36 damage to a single target (6d6+15); the above fighter deals 40 (10d6+5). So it actually scales similar to 5e.