I think her Q should keep applying on hits, BUT I think her Q CD scaling should be adjusted further rather than just Hit or Miss, it should scale on the importance of that hit.
- Miss. Hit nothing, no CD refund. AKA what already happens.
- Hit Minion/Monster. 25% Cd refund.
- Hit champion. 50% CD refund (Minor nerf).
- Hit Vital. 75% CD refund. (Buff, but requires specifically hitting vitals which I consider a fair trade for nerfing her in all other cases of using her Q. Could be adjusted down a bit if deemed too much to 70%).
This MASSIVELY impacts her early game power/farming, as Q is on CD more often until the point at which you can ult a target for more vital targets, and makes using Q to put it on CD more. It also makes using her Q as a gap closer on the side a vital isn't more punishing, as it will go onto a longer CD meaning longer until she can reach a vital. It makes her ult a more important part of her dueling as well as in most cases you will otherwise have longer CDs on Q in almost all cases. Perhaps remove the MS in her ult zone (Since her Q is being significantly more amplified by vital hits) to accompany the stronger vital hit impact.