My highschool debate experience taught me to recognize some 'cheap debate tricks' in rhetoric, but the sad truth is they exist because they work. Most of my judges at competition were volunteers without any particular training in rationality or logic. In one debate where the resolution was something to the effect of 'the use of nuclear weapons is always unjustified' (in which I had the affirmative) at the end of the debate the judge gave a speech about his time in the Pacific during WWII, and how his he and tens of thousands of his compatriots would've all died if they hadn't dropped the bomb when they did, concluding that no argument could convince him it wasn't justified. There is no way this caliber of judge is going to spot even basic fallacies.
In general, the form of debate instruction is just a toolkit for effective motivated reasoning. The pre debate research is all about amassing facts that support your position, and to the extent that you also have to be aware of facts detracting from your position, it's only so you can research counterpoints to those facts, or otherwise discredit them. The debate itself is an exercise in whatever the opposite of active listening is; don't take the opponent's argument as a whole, or understand their position in any deep way, just listen to idenify the tiniest inconsistencies or errors, then pull them out of context and attack.
I don't know how it could be improved, maybe if instead of convincing a judge who is not particularly informed on the topic, the goal was to arrive at some kind of consensus? Instead of modeling presidential debates we model supreme Court opinions? Everyone has to try to write a position that actually gets other people to sign on? There are certainly some insensitive issues that would need to be overcome, but at least the focus would be on broad ideas rather than nit-picking, and each contestant would need to think about convincing other high-information participants rather than the lowest information one?
Never done this kind of formal debating, but it feels like the main skill you learn is the exact opposite of rationality: give up caring about an accurate description of the world in favor of extracting the most personal benefits from a preset view.
I'm sympathetic with that view, but think it's far from clear-cut. For example, suppose you model rationality as the skill of identifying bad arguments plus the mental habit of applying that skill to your own ideas. When the former is the bottleneck, then debating probably has a positive effect on overall rationality; when the latter is the bottleneck, it is probably negative. Probably the latter is more common, but the effect of the former is bigger? I don't have a strong opinion on this though.
As an anecdotal point, I have been pleasantly surprised by how often you can win a debate by arguing primarily for things that you actually believe. The example that comes to mind is being assigned the pro-Brexit side in a debate, and focusing on the EU's pernicious effects on African development, and how trade liberalisation would benefit the bottom billion. In cases like these you don't so much rebut your opponents' points as reframe them to be irrelevant - and I do think that switching mental frameworks is an important skill.
There are two distinct parts to this.
1) does competitive debate do a good job of truth seeking (and/or can it be reformed to do so). I'm with many commentators in that I suspect the answer is no. The format is just not suited to it.
2) do some of the skills of competitive debate aid in truth-seeking outside of such debates. Probably, but I suspect those skills come along with habits and attitudes that make them less effective in truth-seeking than if they were learned elsewhere.