Let's analyze Chatter, shall we...
Chatter itself
Chatter is a BP 65 Flying-typed special move that has a 100% chance to inflict confusion in normal circumstances. It does not make contact, therefore dodging the effects of things like King's Shield, Rocky Helmet, and Iron Barbs. It is also a sound-based move, meaning it bypasses Substitute but is blocked by Soundproof. As a Flying-typed move, there are no type-based immunities.
Confusion causes a Pokemon to lose its turn 50% of the time with no sort of diminishing return on punching yourself in the face. As such, it's perfectly possible for a victim to never move until it wears off, giving the Confusion-inducer plenty of time to attack, set-up, or what have you. Additionally, if a Pokemon fails to move due to sleep or freeze, it does not reduce the length of time the Pokemon is confused, AFAIK. (Correct me if I'm wrong there since I rarely bother to confuse slept or frozen Pokemon.) If a Pokemon loses its turn, it also inflicts damage on itself based on its Attack stat, as such inflicting either chip or significant damage. Confusion is also passed by Baton Pass, meaning you cannot BP pivot out of the status.
Chatter Abuses
Chatter benefits both offense and stall. Offensive pokemon can use the free turns to attack or safely set-up a sweep. Or, in some cases, such as Tail Glow Mega-Ray, sweep with Chatter itself. Stall can use the turns to lock down their opponent, recover, and whittle down their health. Balance can, of course, do both.
If a Pokemon can fit Chatter in its moveset, there is rarely any downsides to doing so short of the opportunity cost of using the moveslot for something else, since the 100% confusion effect is very powerful and is only stopped by niche abilities. Lum and Persim berries stop the confusion, but this allows the Pokemon to "break" the berries and inflict other nasty status freely, such as burns from Sacred Fire.
Chatter can be combined with moves such as Nuzzle, Glare, and Air Slash to lock an opponent down, making it even less likely they can ever move. This is especially true for some moves when combined with Serene Grace.
Chatter can be used with Mold Breaker to bypass any of its ability-based checks. It can also be used with Unnerve to bypass berries, though I have not seen that yet.
Chatter can be boosted with Gale Wings to give it +1 priority, allowing common users to confuse common Pranksters before they can act, as well as revenge KO/confuse most sweepers. It also allows slow, bulky Pokemon to safely confuse near anything before they have a chance to attack and threaten the Pokemon.
Chatter can also be paired with Sheer Force for a boost in damage at the cost of no longer confusing, but why would you do that?
Chatter Counters
Chatter is hard-stopped by Soundproof. However, most Soundproof users are Perish Trappers or Boomburst checkers and are frequently vulnerable to some coverage the Chatter users often carry. For example, Registeel is vulnerable to Earth Power and Blue Flare, Slowbro-Mega to nearly any special move, Giratina to Spacial Rend (notable since many Chatter users are Mega-Ray), and Audino, while bulky, isn't bulky enough to take hits well on both sides with even investment. Mold Breaker and Entrainment also bypass Soundproof completely.
The confusion aspect of Chatter is hard-stopped by Shield Dust and Own Tempo. Shield Dust isn't too bad of an ability, but it's most used for anti-Imposter shenanigans by teams with a Serene Grace user. Coverage, again, is also an issue. Own Tempo is used far less and the last legit use of it I saw outside of Chatter checking was a bulky sweeper using Swagger to either confuse the opponent or get boosts from Magic Bounce... back in Gen V. Also, again, Mold Breaker and Entrainment also bypass Soundproof completely.
Chatter Checks
Lum Berry and Persim Berry let the holder shrug off the confusion, letting them act. Problem is, unless you outspeed, which is hard to do against Mega-Rayquaza and near impossible against Gale Wings, these Pokemon cannot switch in safely. And even then, they can only do it once without Harvest or Recycle. Not to mention, Knock Off vulnerability. And even then, there's no guarantee you'll be able to do anything to the Chatter user. Kyu-W might be able to Boomburst Mega-Ray into oblivion, but Primal-Kyo will just scoff at it and Chatter again. As such, berry checks are unreliable checks.
Resistant types, like Registeel or Regirock. However, they can still get haxed down into oblivion by Confusion or plastered by coverage moves while confused. As such, they are unreliable checks.
Dual-Regen core, such as AV Regen Kyo-P and AV Regen Regirock, can switch back and forth while shrugging off damage like it's nothing and ignoring confusion damage. However, the only thing they can reliably do is PP stall Chatter, since confusion hax. Also, the Chatter abuser can also just set-up as they dry switch back and forth, as many carry either Substitute, Tail Glow, and/or Quiver Dance.
Tangled Feet can potentially allow a victim to outspeed and revenge KO a Chatter abuser. But, this ability serves almost no purpose beyond this function and, even then, the 50% chance of losing your turn is still present, making this strategy horrifically unreliable.
So what makes Chatter suspect worthy and not other confusion?
All other generally reliable forms of confusion, such as Swagger and Teeter Dance, are reflected by Magic Bounce, making them risky to use with anything except Mold Breaker, and Magic Coat, which even Mold Breaker cannot bypass. Additionally, they are stopped by Substitute and Taunt. Also, they do not directly inflict damage, thus a Pokemon cannot sweep with the move alone. And finally, Swagger is risky because Lum Berry is a common item and many Pokemon would appreciate the free attack boost.
Supersonic bypasses Substitute, but with 55% accuracy, it requires usage of No Guard, which makes it vulnerable to Magic Bounce. Also, No Guard itself is a risky move because the opponent will never miss your No Guard user either. Additionally, Supersonic is stopped by Soundproof and, since it does no direct damage, give the user a 100% safe switch-in.
Dynamic Punch mandates No Guard to be reliable, costing an ability slot right from the get go. While strong, it has very low PP of 8, the Confusion is blocked by Substitute, and Ghosts, including the very common Giratina, are flat-out immune to it. Also, No Guard itself is a risky move because the opponent will never miss your No Guard user either.
So my stance on this?
Here's where we get to the realm of opinion. And my opinion is Chatter is definitely worth considering to ban since matches devolve into RNG fests when it is applied, its checks are unreliable, its counters have very few functions outside of countering Chatter, and even then they don't always work, and near literally anything in the metagame can run Chatter effectively.
I mean heck, at least with Evasion, No Guard and Unaware could consistently ignore it, Mold Breaker or not, and you could steal the boosts to make the strategy backfire horribly or force them out with a perfectly accurate Whirlwind. And that still got the boot for turning matches into dice rolling contests rather than displays of skill and strategic cunning. Chatter cannot be reliably stopped by any means that I'm aware of, if just because Mold Breaker exists, the confusion bypasses Substitute, and confusion-curing berries only work once without specific moves or abilities.
So, yeah, I'd be in favor of banning Chatter. But again, this last section is just my opinion.