If the passive damage proved overbearing with her ultimate, they'd likely chip the damage on the ultimate.
Exactly! That's my entire problem with it! I hated, hated it when the ultimate's damage used to be compromised for the sake of stacks. That entire concept of reducing the ult's damage so that it can be backloaded with a stacking mechanic sounds like absolute fucking bullshit. That is the reason she felt like crap in the past, and I hate the idea of it returning with a passion.
There is nothing good that can come of attaching this passive to her ultimate. This is a purely negative idea. No positives, only downsides. The ultimate's damage should not be backloaded. There should be a threat to any amount of time spent sitting in the ult. I shouldn't be able to get out after 3 ticks and be nearly unscathed.
In terms of function? Yes, it's fine
It's better than fine. It's unique. It's something we don't have otherwise. It is different. Single-target damage though applying stacks is not unique. It's overdone. It's generic. It's boring.
So, I'm seeing a downgrade in gameplay, which you are justifying.
For thematic as a character and as a marksman it is horrible.
As an ADC, it's perfectly fine. She perfectly fulfills the criteria for being an ADC. All that she needs to "thematically" be an ADC is ranged AD autoattacks. She doesn't need to have some major focus on single target. She doesn't need a stacking mechanic. All of that is needless limitations. All she needs is to be a ranged physical damage dealer. That is the only criteria that matters.
As for her character thematics: First, I don't really care that much. I care way more that her gameplay is unique, and I think your proposal is a major downgrade in that department. That alone makes it a bad idea to me. If we're going to change her gameplay to fit thematics, the gameplay should be at least as good as what it currently is. The ultimate changes alone guarantee that this would not be true. We're going back towards a design that already failed spectacularly.
Second, I think they're fine there too. I don't see any particular reason why "single target damage" is the twin gun thing. AoE seems to be perfectly fine. She's the girl who blasts everyone down. Sprays and prays. Works for me.
I'm not trying to be facetious here. I've seriously never seen any disconnect between her gameplay and thematics. You're taking it as granted that this is something that is a problem, but I don't see any issue with it. When I picture a double gunner, I see them shooting as many different people as possible. That's the entire point of having multiple guns, so you can shoot a lot of people.
Here's a scene from Equilibrium that I feel best defines how a gunner dual wielding pistols should, to some extent, be fighting.
He shoots a lot of different people. Seems to fit the current paradigm quite well.
How does a stacking mechanic fit what I just watched? I see nothing that made me think anything about shooting the same person over and over again. That seems like the opposite of what I just saw. I'm seriously even more opposed to your proposal after seeing that video.
It's almost making me question why Lucian doesn't have more of an AoE focus. We could do that with his double guns pretty well I think. That would fit the video much better if we took away some of his single target damage and introduced some way to shoot multiple people. He has the trenchcoat thing going on too.
is the only one who truly has one. The only other marksman who even comes close is 
due to his poison.
because hers is tied to a targeted skill. I don't count 
or 
because theirs are based on their attacks, rather than on-hit. 
doesn't count either because it requires that he casts a skill to make full use of it.
