Let's organize a tournament.

I think the captain selection process is quite straightforward.
It would be more interesting to make the group stage in two phases... with groups of 6 people. The top 4 advance to the next round. The "weakest link" is eliminated, just like in the TV show.
These are just my thoughts.

I don't think the issue of captain selection will be a major problem, because essentially the captains will only perform one function in this tournament: the initial team selection. However, to ensure that this selection is made appropriately, it would be best to appoint players as captains who have a good understanding of the gaming abilities of most participants.
I don't quite understand the idea of group stages and what their purpose is in relation to the concept of this tournament.