While not such a bad idea, having something like this replace the damage an ability currently has could be problematic. Take Jhin for example. His Q already does something similar to your suggestion. But his ult would not be a good spot for it unless it did not significantly hurt his damage if a shot is missed. He has only 4 shots, all of which are pretty telegraphed and can be dodged pretty easily if you move correctly. So by having the damage be requiring of you to have 100% accuracy is a fairly huge nerf in this case. Plus it would then put him in a situation where he has to choose between hitting a massive tank who would be a waste of a shot but a safe target to reliably hit, or risking his damage aiming at a priority target like he should be, but risk missing given their often smaller hit box and/or increased mobility. A flash or some other mobility, or even minor latency, would more or less kill your damage for what is your ultimate ability. Now, something like Lucian's ult, where stacking could be applied significantly easier given its multiple shots where basically the stacking would reset after each miss (I know that this is slightly different than how you put it), I could see it working well with.
All this being said though, I would say that implementing this as a common occurrence would not be such a good idea. By tying an ability's damage into accuracy would make skill shots have even more risk (cost to use, animation timing, cool downs, etc... and now a lowering of damage) for only a minor reward (slight increase in damage). Also by requiring accuracy, it hurts new players (to the game and/or champion) and players who have less than ideal connections. In other words, regardless of the skill the player has for the skill shots, where even if it is not their fault they missed (target dodges, latency, D/C for a second, etc..), they could be punished damage wise for not landing it. Skill shots are already having to deal with these concerns. But they do not have any requirement of maintaining accuracy. By adding that necessity for the ability to be effective, it just hurts the ability more so than it helps it.
is a great example. His Q is basically what you are asking for. If he catches his ax, he keeps his damage buff, if he misses, the buff is dropped. Now, that damage is pretty significant to his kit. So by having this interaction, it forces him to "work" to keep it. But, lets say that instead of him catching his axes, his basic attacks now become skill shots and he has to hit every single one to keep his damage. It is a much different situation now. He has a buff where he is sharing the requirement of keeping it, with his enemies. Now it is no longer entirely up to him to catch his ax, it is now him having perfect accuracy AND his enemies not being able to dodge them even once.