Willie the Duck
Legend
This seems like more things to track and more tactical considerations to take into account (both for you and your opponent), and could potentially exacerbate the wait between turns that make a 'miss' turn so frustrating. I can see the reason to want it, but one would have to be very sure that the juice is worth the squeeze.
Note also that, as long as combat rounds can get, 5e tends to give (or at least allow) multiple, often non-interdependent actions per round. If you are the type of player that really chaffs at having no impact, you can make a character that has a hard time not doing anything. Star druids can do their main thing, but then almost always use a bonus action to shoot (not dependent on rest of actions being an attack). Reach fighters with Sentinel or Polearm Master regularly get an activity on their opponent's turn. Anyone with a 'pet' (class feature, magic item, spell, or 'and you play the NPC') can get a whole second set of actions, sometimes costing part of your action, sometimes not.
Regardless, I think this might be better for developing a new game (where you can put the 'or on a miss' math into the development of each ability). Current abilities that grant nothing on a miss/successful-save-against are generally pretty strong, and granting a uniform bonus to them* is probably not the most balanced thing for the game as-is.
*that isn't of trivial value, and if so then what's the point?
That said, it is not, in and of itself, a bad idea. Building effects with effect A on a success and lesser effect B on a failure is a nice model, one that D&D does rarely (usually in the form of damaging/hostile effects which are still rough terrain even if resisted).
Note also that, as long as combat rounds can get, 5e tends to give (or at least allow) multiple, often non-interdependent actions per round. If you are the type of player that really chaffs at having no impact, you can make a character that has a hard time not doing anything. Star druids can do their main thing, but then almost always use a bonus action to shoot (not dependent on rest of actions being an attack). Reach fighters with Sentinel or Polearm Master regularly get an activity on their opponent's turn. Anyone with a 'pet' (class feature, magic item, spell, or 'and you play the NPC') can get a whole second set of actions, sometimes costing part of your action, sometimes not.
Regardless, I think this might be better for developing a new game (where you can put the 'or on a miss' math into the development of each ability). Current abilities that grant nothing on a miss/successful-save-against are generally pretty strong, and granting a uniform bonus to them* is probably not the most balanced thing for the game as-is.
*that isn't of trivial value, and if so then what's the point?
That said, it is not, in and of itself, a bad idea. Building effects with effect A on a success and lesser effect B on a failure is a nice model, one that D&D does rarely (usually in the form of damaging/hostile effects which are still rough terrain even if resisted).

