I'd like to remind you that I paid for the use of this bracket software, and I fully expect ongoing revisions and upgrades. https://mariogames.io/

I wish for this feature to report stats as Teams and also individual performance in the tournament.
Challonge.com can win a lot of users by this.

This would be really nice if you wanted to change team members around for a round robin style tournament.
Round 1 AB vs CD
Round 2 AC vs BD
Round 2 AD vs BC

Am I understanding the suggestion correctly?

Shuffle Seeds is only effective with individual players and teams that have already been formed. A tournament, such as a blind draw, requires individual players to be randomly placed into teams. As for the suggestion to use an additional webpage/program to perform this function, I respectfully remind you that I purchased the use of this bracket software and I fully expect continuous revisions and upgrades. I'm working towards simplifying this process, not creating additional time consuming steps.

I'm not really sure what you mean, but the "Shuffle Seeds" button randomizes seeds. If that doesn't do the trick, I use RANDOM.ORG's List Randomizer, removing each team from the list after it is drawn until there is one team left in the list.