AI-assisted debate helpers take away from the sport and spirit of productive argumentational skill-building in terms of articulation of one's actual position and the need to give a cogent account for why the speaker actually holds his cherished beliefs. Having someone else argue for you (in this case, having a non-sentient language emulator do your argumentational homework) looks objectively bad and should be actively shunned and discouraged.

I wouldn't enforce it as a universal rule, but my general attitude is one that is based on practical experience: usually, people who heavily rely on AI do not develop the skills necessary to be strong debaters, and they always fallback whenever a serious challenge is posed to them that they are unable to give an answer for. Inevitably, it ends up being used as a crutch, and so I'd be more in favor of discouraging it until people demonstrate that they are able to utilize it in a responsible way. The people who are most notorious - call them "AI debaters" - can always rely on the bot to think for them and upholster otherwise weakly defensible positions with a veneer of formality and technical depth.

Organizing your thoughts can occur without AI assistance. People do it all the time. The problem is that AI automates the task so that the need to develop that skill is offloaded when it ought to be honed and developed to its fullest extent. I think that people who rely heavily on AI very rarely if ever have the motivation or discipline to develop those skills on their own, and AI assistants only expects them to do the bare minimum. People who lack the ability to organize their own points also lack the ability to have strongly well-formed views. Luckily, those skills can be entrained. This means that AI can be a sparring partner at best. For competitive debating, it can be seen as a form of cheating. Just like using AI assistants in other competitive games (Chess or Poker) would be considered cheating, giving the AI user a potentially unjust advantage.

Like I've said, those skills can be developed, and AI can help aid in developing those skills, but it should never be used as a crutch. And that is what people are doing. They are using AI to do their own homework and never taking the time to develop those skills because they can simply offload them to a language-based neural network. The situation calls for better programs which can infuse those skills through active training protocols and procedures (some of which might even involve the use of AI to a limited degree of assistance) without therefore delegating all the important cognitive tasks (organizing and structuring your arguments) to an insentient machine.

Those who lack those skills can still improve by specifically targeting those aspects of language and communication that they struggle with. But I think that it's also unfair for people with a weak epistemology to have undue sway over others just because they happen to be able to wield the engine efficiently. In any other competitive arena, using an AI assistant is always considered cheating. Debating is a little different, but it's not significantly different enough to make the use of AI something worthy of encouragement or support.