It is too close to gambling or promotion of gambling in some jurisdictions.
Tournaments
IANAL. Write couple of paragraphs explaining exactly what do you mean by "bracket" and why it would be "so much fun".
So what i'm saying here is that it would be fun to do bracket tournaments like the one below: 
the reason they would be so much fun is that you can compete like professionals in a way and have fun at the same time. You could also make it like a club tournament to decide seating's for every player in the club and also because its so fun to compete like this, like you get to feel how tournaments can be like and that you can keep going and still get second (or third) even if you lose first round and get sent to the losers bracket. or even just a standard elimination bracket to keep the stakes high while still having fun competing.
I repeat that IANAL.
Here are the three examples of "brackets" that caused C.C legal troubles outside of the former British Empire and its former colonies (like the USA).
https://www.chess.com/news/view/chess-com-global-championship-100k-bracket-contest
https://www.chess.com/news/view/2024-ccl-prediction-bracket-challenge
https://www.chess.com/news/view/2024-fall-ccl-prediction-bracket-challenge
In some places uttering the "void where prohibited" or "no purchase necessary" incantations is not a valid legal defense.
Edit: Added more examples.
first off I am not saying anything that makes me expect that you are a lawyer, okay? Also what I'm saying is that you and a club or some friends play in a tournament, and you make it so that there is no fee to join or play or any there is no fee at all, basically I'm suggesting that along with the Swiss and Arena tournaments we add a bracket style one, that, may I repeat, does not cost any player or person any money to do. and don't have prizes besides the little medal you get sent for achieving 1st, 2nd or 3rd like in the Swiss and arena tournaments.
It is not EXACTLY the same, but having a daily knockout tournament set up with groups of 2 .... is kind of similar. In a way.
Automatically associating a bracket system of pairing with gambling is quite a stretch, and says more about the person making that "connection" than it does about the proposal itself. That some people may associate brackets with betting has nothing to do with the validity of the pairing system. There's not a single thing within the pairing system itself that somehow explicitly encourages gambling. Citing examples of bracket-system events that are associated with betting doesn't prove any point.
Why doesn't chess.com have a tournament bracket? I mean wouldn't that be so much fun to play a bracket with your club or with friends?