I am of the position that:
Your brawl team should be tied to something tangible for the brawl to make specific challenges of. If we tie brawl teams to the elements then we need to make the elements internally relevant. If we do not tie them to the elements then we need to tie them to something else.
The solution is found related to the team name. Each team in addition to choosing a team name will choose a brawlmaster approved team theme.
Look at our team names: AbSTRACT, Entropony Cowboys, The Crusaderps, Fire, Expensive Clocks and Surf Ninjas
With the exception of the overly general Team Fire and the overly specific Team Entropony Cowboys, each team name could easily be matched with one of a dozen potential themes.
AbSTRACT might choose Abstract Ideas as a theme. This would translate for the card designer to Cards with abstract ideas. Maybe this would be a bunch of creature metaphors. Or maybe it would be abstract ideas captured in the medium of spells and skills.
Team Entropony Cowboys would of course have chosen a theme in no way related to Entropy, Ponies or Cowboys. (They are entropy what did you expect?)
But you mention the bosses have an element assigned to them? Go with volunteers. Have us, the minions, continue to judge the worthiness of bosses during ties in the auction. Do not tie elements to the bosses. Masters can compete as Bosses but other players can also complete as bosses. If there are too many bosses then some might be eliminated/moved to the minion pool. However only worthy bosses should remain. This might mean a master is eliminated. (Of course, Trials should ensure all Masters are worthy Bosses but that it not always the case.) Also there is worthy and there is Worthy.
Now to address the guilds:
1) Each player on a winning team earns points for the guild they are part of. "Team Fire" Could have been 6 Water Guildmates if everyone but the boss were all of guild water. Not really a team fire if 6/7ths are water. If the players and not the teams should be tied to guilds then the Guilds are no reason to tie the teams to elements.
2)I really don't want it to be standard practice to