Bell curve rolls and margin of success as damage/effect base exist since forever, not only in rpgs. They have their issues too. For example, it's really hard to roll higher than the average, so each point of DC added is not just a 5% less chance to succeed, but an exponentially lower chance instead. To roll a 10 on 3d6 or a d20, you have a 55% chance, but to roll a 15, you have only a 9,26% chance, far less than the 30% for a plain d20. With 3d6, you would get no chance to roll a 19 or 20 too. Also, if you use margin of success, you can't also have a critical hit system in place, since they could mess with each other. There are many games that use either or both of those mechanics. In Italy we have Lex Arcana, which uses both for different things: margin of success for damage, and you have a choice of how many and what types of dice to roll for a check, given that there is an exploding dice mechanic too, that is rolling the max on a dice means rolling them again and adding the result. This latter trick is what replaces standard critical hits. Since you decide what to roll, sometimes it may be better to roll a single dice, since you have more chances to score the max than by rolling multiple dice, while other times you may prefer to roll many dice, since getting an average score would grant success in a crucial check. That said, they do not work well in D&D-style games. The attack roll is just a way to see if you hit or not, while how well you hit is in the damage roll. The d20 roll is basically a percentile roll with 5% steps, so you are basically trying to roll your chance to hit or less on that die. It's a "yes or no" kind of mechanic. There is no real place for a margin of success mechanic in that, unless we place a certain percentile chance to roll a crit in addition to that, which ends up being a better result, especially in those games with damage multipliers on crit. But again, how well you have critically hit is in the damage roll, not in the attack roll. Another thing against bell curves in d20 games is the difficulty class, which goes up or down in a linear way, not in a gaussian way. The whole difficulty system would need a complete rework, otherwise combat would become incredibly harsh when multiple bonuses to defenses start to add up. Where the bell curve works well is in games with fixed scores, for example between 3 and 15 and you have to roll your score or less on 3d6. The trick here is trying to get most of the chance to succeed, while trying not to send the target number below the middle score due to penalties, because the most you get far away from the average, the harder becomes to succeed, really, really fast. Where the margin of success works well is in games with exploding dice, dice pools, or other unconventional and non-linear ways to determine success, where you can easily go beyond what you need to succeed or where you can succeed multiple times with the same roll.
Bell curve rolls and margin of success as damage/effect base exist since forever, not only in rpgs. They have their issues too.
For example, it's really hard to roll higher than the average, so each point of DC added is not just a 5% less chance to succeed, but an exponentially lower chance instead. To roll a 10 on 3d6 or a d20, you have a 55% chance, but to roll a 15, you have only a 9,26% chance, far less than the 30% for a plain d20. With 3d6, you would get no chance to roll a 19 or 20 too.
Also, if you use margin of success, you can't also have a critical hit system in place, since they could mess with each other.
There are many games that use either or both of those mechanics. In Italy we have Lex Arcana, which uses both for different things: margin of success for damage, and you have a choice of how many and what types of dice to roll for a check, given that there is an exploding dice mechanic too, that is rolling the max on a dice means rolling them again and adding the result. This latter trick is what replaces standard critical hits. Since you decide what to roll, sometimes it may be better to roll a single dice, since you have more chances to score the max than by rolling multiple dice, while other times you may prefer to roll many dice, since getting an average score would grant success in a crucial check.
That said, they do not work well in D&D-style games. The attack roll is just a way to see if you hit or not, while how well you hit is in the damage roll.
The d20 roll is basically a percentile roll with 5% steps, so you are basically trying to roll your chance to hit or less on that die. It's a "yes or no" kind of mechanic. There is no real place for a margin of success mechanic in that, unless we place a certain percentile chance to roll a crit in addition to that, which ends up being a better result, especially in those games with damage multipliers on crit.
But again, how well you have critically hit is in the damage roll, not in the attack roll.
Another thing against bell curves in d20 games is the difficulty class, which goes up or down in a linear way, not in a gaussian way. The whole difficulty system would need a complete rework, otherwise combat would become incredibly harsh when multiple bonuses to defenses start to add up.
Where the bell curve works well is in games with fixed scores, for example between 3 and 15 and you have to roll your score or less on 3d6. The trick here is trying to get most of the chance to succeed, while trying not to send the target number below the middle score due to penalties, because the most you get far away from the average, the harder becomes to succeed, really, really fast.
Where the margin of success works well is in games with exploding dice, dice pools, or other unconventional and non-linear ways to determine success, where you can easily go beyond what you need to succeed or where you can succeed multiple times with the same roll.
My game is utilizing a d20 roll under mechanic and like you damage is based weapon type and difference between challenge rating and the result.