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For example single type, focusing on a single Pokemon, or focusing on a specific stat
https://pokemondb.net/platinum/gymleaders-elitefour

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What does your link have to do with your question?
I think it's saying that most bosses in Platinum use Pokemon of a certain type or Pokemon with a certain high stat, and then asking whether Colosseum or XD do anything similar.
Also this question might not be answerable. If the bosses' Pokemon really are completely random, how can we prove that they were completely random?
Where is the randomness part coming from?
If the teams really don't follow any theme, how can we prove that they don't follow any theme?
The four trainers before Nascour in Pokemon Colosseum have type themes and the final boss in pokemon XD uses all kanto pokemon besides Lugia. That's two I can think of, but I know there are more that have certain themes.
You don't need to prove the teams are random, you just need to show that they do or do not centre around a particular type or stat.
If the flag is for a different reason then let me know. I have not played these games.
Is it okay if I define "theme" as something that's shared by more than half of the team, or shared by the highest level Pokemon and at least half of the team, and ignore teams that have only one species?
If this definition is good, then I think these are all the "theme" teams in Colosseum.
Miror B: water, grass, special defense (his team is 80% Ludicolo, and his other Pokemon doesn't fit any of these "themes")
Skrub: physical defense
Dakim: ground
Ein: speed
Gonzap: physical attack
Evice: physical attack
Gonzap: physical attack
Miror B: water, grass, special defense
Agnol: physical defense

Resix: fire, special attack
Blusix: water
Yellosix: electric, special attack
Purpsix: poison, HP
Greesix: grass, physical defense
Naps: physical defense
Lovrina: speed

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This answer defines "theme" as something shared by more than half of the team or shared by the highest level Pokemon and at least half of the team. It also ignores teams that have only one Pokemon species. "Themes" marked "(all)" are shared by the entire team.

Colosseum:
Miror B: water, grass, special defense
Skrub: physical defense
Dakim: ground
Ein: speed
Gonzap: physical attack
Evice: physical attack
Gonzap: physical attack (all)
Miror B: water, grass, special defense
Agnol: physical defense

XD:
Resix: fire (all), special attack (all)
Blusix: water (all)
Yellosix: electric (all), special attack
Purpsix: poison (all), HP
Greesix: grass (all), physical defense
Naps: physical defense
Lovrina: speed
Exol: normal
Snattle: HP
Justy: ground, physical defense
Eagun: electric (all), speed (all)
Miror B: water, grass, special attack

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