It wouldn't work in all situations. It would also reset her E in situations where it shouldn't be reset (according to the current design). For example, let's say cassy poisons champion A who is low health. Cassy then casts her E on champion B who is not poisoned which puts it on cooldown for a couple seconds. Champion A dies, giving Cassy the reset on her E even though she didn't really deserve it. The same thing occurs if she Es target A before applying her poison, then A dies to poison that she applies afterwards.
Another problem with that is that Cassy's E can reset from poisons that don't come from Cassy. For example, let's say singed has a target poisened that Cassy Es. The target dies before her E lands, but since it wasn't her poison that killed the champion she doesn't get the reset. Had the E hit she would have.
The last thing is that she still suffers from the original problem. If she isn't the one to get the killing blow then she doesn't get the reset. This time she just has an extra two sources of damage to get the killing blow with.
So yeah, it would work in some situations, but it wouldn't work in a lot more. I appreciate the input though.