Just look at Melee where CC really isn't that relevant at high/top level play all that much despite the mechanic being identical.
Are the relevant characters in Melee weak to CC ? No.
-Spacies have un-CCable shines and dairs,
-Fox, Marth, Sheik, CF and ICs have extremely strong grab combos, you could even say grab is their main combo starter and people wouldn't laugh too much at you.
-Peach has dsmash,
-CF has Stomp,
-and all of them have standard grabs.
Are there characters which are weak to CC in Melee ? You tell me, I don't play Melee. But if the answer is yes, those are not relevant characters, those PM is balanced around. Is the fact that they are weak to CC the reason they are not relevant characters ? You tell me
And, sure, Ivy's game plan is not nearly as advanced as any of those characters I've mentionned above. CC is the kind of mechanic that invalidates moves, so you just get kinda used to never inputting the moves that are weak to it after 10+ years, and rely on the rest of the character's toolkit instead.
However, CC has been one of Ivysaur's main weaknesses ever since her release in 2.5, so it has been a strong point of focus for us to push the character. It invalidates so many of her moves that it was either "let's become razor leaf - the character" or "let's try to find answers to it, dammit".
We've tried our damnest to push her past this because it was one of the most obvious things we'd have to do to do anything with the character. There's
this thread I started working on in 3.02 but never got to finish before quitting PM, and
countless skype discussions on the topic.
And the opposite could be said. I can't count on my hands the amount of sets I've seen Machiavelli win against top players who didn't CC any of the relevant moves. It's even worse for JZ, every single Ivy main I've talked to is like "what he's doing
should not work, wtf" (we've found some of the reasons his playstyle works since then, but the him never getting CC'd part is still up for grabs)
So let's look at Ivy :
In general, Ivy's moves are mostly multihits. There are a couple things you should know about multihits and Ivy in general :
-Firstly, look up the difference between CC and ASDI down if you haven't already. Long story short, CC is a stronger version of ASDI down, but it can only be done by actually crouching, so when you get whiff punished, the best you can do is ASDI down. Multihits break this flow. Depending on the move, either it always gets CC'd, or it always gets ASDI'd down. This conditions how dangerous the multihit's strong last hit really is (the one that matters most, the one that decides if you get punished on hit or get a follow up) : if the move can always get CC'd, then the last hit of the move is much less powerful, and can sometimes be punished on hit. It just so happens that Ivysaur has quite a few of those moves you can always CC. Even Ivysaur's notoriously "good" nair is one such move. Can't say about 3.6 ftilt since I have not played 3.6, but 3.5 ftilt and 3.6b ftilt worked that way too. Oddly enough, Ivy's jab and bair do not work that way : either you CC both hits (in which case why didn't you punish between the hits ?), or the best you can do is ASDI down the second hit.
-Secondly, there really are two kinds of multihit moves : the ones which allow you to move, and the ones which do not. If you can move, you can follow the opponent's SDI so there's a lot of interaction going on and it's pretty interesting : Ivy's nair is a good example of that, despite the "always CC" part. If you can't, those SDI multipliers better be low, because if they aren't you can probably get punished on hit by every character in the game, at every %. The only way to use the move properly and safely becomes "miss the first X hits on purpose so that the opponent doesn't have the time to SDI it". Again, Ivy's ftilt was notorious for this in 3.02 and 3.6b, can't say about 3.6 but it's probably the same.
-Finally, people CC for two main reasons : to punish, and to break combos. Generally speaking, if they're CCing in close quarters, it's the former, else it's the latter. Having your combo broken by CC is okay, mostly : you do not get hit back. You just get less bang for your buck than you otherwise would, but still get stage position, frame advantage, that sorta things. CC-punish is the thing you want to have tools against. Having no tools against this is like having no tools against shield grabs, in a sense. And being a "long range multihit" kind of character, Ivysaur happens to have a few moves that only break CC at a distance, and thus are not really useful against CC-punishes. Things that have tippers, such as dtilt and bair, have this property. Slow but powerful moves, such as fsmash and grab, also have this property. Fair would be in that category too, except it just sucks against CC in general, not being able to break it until 80% even with a proper tipper and all.
The old dash attack's strong hit was strong against CC. The new one not so much, it sends opponents backwards sometimes so that it doesn't combo, etc... The even older dash attack was even better because it could gatling combo CCers into a sweetspot usmash. But since Ivysaur's dash attack is frame 4, she's one of the very few characters who got super screwed over by 3.5's changes to DACUS mechanics. She can't gatling anymore. Any faster than that and you can still gatling, any slower than that and you never could in the first place : frame 4 dash attacks are the only ones which were able to gatling, and lost that ability.
So right now, Ivy's best tools against CC are probably nair-roll and a frame 8 dsmash that doesn't actually break CC-punishes so much as it pushes the victim too far so that their punish whiffs, lol.
Finally, there's razor leaf. I feel like people have gotten a much better understanding of this move than in the past, so it shouldn't be too surprising if I tell you this projectile sucks vs CC. Tell me if it is, but the explanation is going to be god damned long, razor leaf is many things but it is not shallow.
There's a LOT more to say about the topic of Ivy vs CC than I could possibly cover in a readable fashion. But that's the gist of it imo.