You'll be lucky enough to even have the mana to get half of them off. Her manacosts are downright absurd and entirely unreasonable after losing her old passive.
Um at rank 1 Cassio's Q had it's mana increased from 35 to 40 mana per cast.
Mean while at rank 1 Cassio's E had it's mana cost reduced to 30 from 50, in fact at all ranks but rank 5 twin fang now costs less than it cost old cassiopeia 30 / 45 / 60 / 75 / 90 now compared to 50 / 60 / 70 / 80 / 90. pre-rework.
So to put that into context, 1Q+3Es previously would have cost you 185 mana
Now 1Q +6Es costs 220.
She starts with 270 mana +60 for each level so at level 2 she will have 390 mana without any runes/masteries. That will leave you with 170, still more than enough to poison the minion wave after and E to last hit for mana regen which at level 2 will be the 30 mana cost of your twin fang +11.7 from 3% boost +4 per kill from the doran ring.
While if you get all 6 Es off it will cost slightly more, all of 35 more, it doesn't suddenly cripple you like everyone is trying to say it does. Hell you could still Q and cast 4 more Es on the enemy laner before going oom which is more than enough to kill pretty much anyone in the game at that level.
You're crazy if you think it's an automatic 6 Es now, you won't get 6 and at most you'll land 1 more than before if any more. If you can land 6 now you would have landed 5 before. More realistically you'll land 3 now at low levels or 4 if they're going straight into you, in that case it would have been 3-4 before as well. They're not going to stand still and let you get off every E you can while your poison is ticking.
Your math is based on an imaginary scenario that doesn't exist.
Um in the past it was impossible to land more than 3 Es because of how the resets worked. It didn't reset until the E actually hit the target meaning you had to wait for the travel time and then you had to wait for the CD after it reset to .5 seconds. This tended to mean the CD was 1 second between the travel time and the reset and only really changed if you where point blank range. Now the CD resets to .5 instantly upon cast if the enemy target is poisened. This means the ticker begins before the E has even dealt it's damage and without travel time that leaves the spell with a flat .5 CD which makes it more than possible to get 6 Es in if you position correctly and are smart casting. I generally sit between 100-150 ping and I am consistently getting 5 Es in with each Q. It isn't some imaginary scenario it's something people like Cobra and I, and I'm sure others who are not on these boards, are doing consistently because of how we position and play around her E spam play style. We realize how much damage it really does vs how much other champs can do and take advantage of the fact that we are stronger than they are and punish those who don't respect it.
Really when you put it in context it makes sense why so many Diamonds show so much respect to Cobra in his videos. Chances are they realized Cassio can out DPS them and that Cobra will punish them if they try to fight, vs players in Bronze/Silver/Gold who continue to think Cassio does zero damage and is trash and disrespect her while playing against Cassio's who feel the same way and allow themselves to be disrespected. As long as you continue to insist that she is weak you will never realize just how strong she really is. I've provided the numbers and the data to show that she does in fact win against pretty much anyone when played correctly, if you don't want to accept that and abuse players that disrespect you when playing her that is on you, not the champion.