i have a suggestion for lichess.

Take the average rating of the 4 players that would qualify for Sections <2400 <2200 <2000 <1800 <1600

Works great for the USCF National Team Championships. There are parameters, such as players rating on a team must fall within a certain range. (Can't have 3 highly rated and 1 very low for example)
Highest rated plays Board #1 on down to Board #4
This allows for the members of a team to be approximately the same strength playing another team of similar strength. (Which also allows your alternates to be of similar rating.)

lurarose wrote:
"The problem with such tournaments is they bring out the cheaters in droves. People from economically bad off (socialist) countries such as Venezuela would come here in the hundreds using computer engines to try to get at that prize money because it beats waiting in a bread line."

I can picture the likely scenario:
VenezuelaBoy (VB). Dad, I want to learn to play chess.
VenezuelaDad (VD). We are poor son. No time for frivolous pursuits. Today you must go and stand in the bread line.
VB. But Dad, I can make money!
VD. How so son?
VB. By cheating !
VD. I've taught you how to rob and steal, but cheating I will not tolorate!
VB. But Dad? It's $100 US dollars!
VD. WOW! That much hey. What do you need?
VB. Well, for starters a laptop and the very best chess software.
VD. How will you manage this?
VB. I'll steal it.
VD. Good job son. But you don't know how to play chess.
VB. Oh, that's the easy part because I'll be cheating. I won't really know how to play.
VD. My percentage is 50%
VB. Nice try Dad, but it was my idea. $90 for me, $10 for you and next week you stand in the bread line because I'll be on a boat to the USA !

+1 for both

@Toadofsky "I've repeatedly asked in this forum how that second idea would work"
For start I think the simplest and most feasible implementation of team tournaments would be in correspondence chess where the scheduling is not as problematic because one move takes several days.

The team leaders could assign the opposing players, a winning player get 1 point for his team the loser get 0, and that team wins who has more points from the matches (like in Chess Olympiad).

Later if this system works well, could be expand to other real time formats as well, like in Lichess 45+45 League.