To clarify, the readability problem with AoE damage over time is that in complicated team fights, it becomes especially difficult to track/appreciate the source of the damage, but more importantly it's nearly impossible to understand how much damage you are going to take or how to play around it.
In team fights, the burst is also approximately untrackable. I... I don't think that that's a problem, since as you say, they're usually very strong visually and thus easy to see "this shiny/big explosion did lots of damage", which I agree is something that Cassiopeia... doesn't have, her visuals are somewhat piddly comparatively.
When you get edge'd by the hitbox of one of Cassiopeia's poisons, you tend not to notice, and then suddenly end up with a third of your HP gone without even knowing what happened or how to do better next time. This is the nature of these longer lasting abilities. At the same time, making these abilities as loud/readable as other, non-lingering spells would incur huge visual clutter costs because of their sheer volume and uptime (imagine if Singed's poison trail was opaque).
Maybe prepatch, but now many people ignore it because it's ignorable. Should some sort of balance not be struck? I get that that's a gameplay thing, but with Cassiopeia her thematic and gameplay are intertwined. Her old self with high poison damage was really good because it felt like an underhanded diplomat of sorts, somebody waiting for the right time to pounce. But Cassiopeia makes that weakness herself, and it felt really nice and offered some fulfillment there.
W ends up being a bigger culprit than Q here, because it is effectively undodgeable, covers a large area, and lasts an exceptionally long time.
... What? Miasma occupies a large area when you throw it out? I think that the fact that it slowly expands makes it not cover as large an area as it first seems (just looking at the min/max size numbers that is).
Basically, with the spell's readability, dodgeability, and duration profiles, it occupied a much lower portion of the opponents mind-space than it should have, given how threatening it actually was.
This is less a point of mastery ("opponents should just learn that Misama is threatening") than it was the spell dealing inappropriate damage given how it was applied.
... What? I'm sorry, WHAT? What are you trying to say because I'm pretty sure that "the spell [was] dealing inappropriate damage given how it was applied" was not it. Do you mean that Miasma dealt too much damage for a thick cloud of purple fumes floating above the ground? Toxins tend to be small in the first place... or do you mean that Miasma, as an AoE DoT-applying field, was dealing too much damage? I really have a hard time agreeing with that seeing as it took place over 9 seconds, and it is/was very easy to just walk out of it and take much less damage from it. But now walking out of it is (mostly) pointless because in lane it barely does more damage than one's HP Regen, since Cassiopeia HAS to build mana items so she can actually last hit enemies, which means no AP for her LOW AP scaling W.
The Twin Fang poison amp does add some under-the-hood stuff, which is a clarity cost, but ultimately it's a net gain. When you get hit by the tip of one of Cassiopeia's more difficult to track abilities, you won't be as punished unless she very clearly declared that you are going to take a lot of damage (by hitting you with Twin Fangs). This way, when you're about to take a ton of poison damage, you understand why and where it's coming from.
The thing everybody has been telling you this rework needs to stop doing is good for game health. Ok, sure! It's better if enemies know where Cassiopeia's damage is coming from.
#Why can't it be "because I got hit with this explosive green thing" or "I am standing in this purple cloud" instead of "Cassiopeia is walking up to me and throwing twin blades of energy that are about as large as her torso"? It was pretty clear before that one took damage because you were hit by Cassiopeia's poisons.
That's the theory anyway, and it seems to be working out. The Twin Fang amp does some other stuff as well, like add optimizations to her trading patterns and emphasize the importance of using both of her combat ranges, but that's the clarity reasoning.
She has, effectively, one combat range, due to how weak her poisons are. It doesn't matter if she has 850 (or whatever it is) range on Noxious Blast when Noxious Blast alone does nothing. Noxious Blast followed with Twin Fangs followed with Noxious Blast does make that last Noxious Blast deal a fair amount of damage, but from the perspective of the Cassiopeia player it is still damage from Twin Fangs and not damage from Noxious Blast.
That all said, un-amped poisons might simply be doing too little damage as it stands, and the answer might be to add some poison power back there.
And everybody has been telling you that this is needed since this rework was pushed onto the PBE.
p.s. I don't play Cassiopeia, and her DoTs were definitely easy to understand because "I got hit with green thing so now I'm taking damage". They were easy to appreciate for Cassio, too, as "I hit my poison and I now see enemy health trickling away *evil cackle*". I find the reason of "Poisons are hard to appreciate" to be entirely BS because anybody that things a strong DoT is weaker/less able to be appreciated just because it's a DoT and not burst (the difference is basically 0 if you're poking enemies) is somebody that needs to learn strategy games better.