Well there's one problem I see with complete liberty of choosing: upgraded cards.
During deckbuilding phase you take into account the upgraded cards an opponent can use, while this would eliminate that since you don't know whether they will. Technically, all teams could gang up on one poor team - who has done nothing wrong - to eliminate them asap (8x general hurts so bad).
Just more spread out randomness please, upgraded cards can make such a huge difference...
The current system doesn't prevent teams from being ganged-up on (see Death in Round 2).
And the fact that upgraded cards make a huge difference is completely the point. RNG decides your General is facing an Element where the perfect counter deck to play works just as well unupped as it would with 6 upped cards. Meanwhile you have a match against another element where you can play a perfect counter if only you could up 3 or 6 cards. Why is it bad to allow teams to have flexibility? Your argument seems to me to just be saying that adopting the system I proposed would make it harder to predict what you'll face and harder to prepare perfect decks to go against it. Harder and less predictable isn't necessarily a bad thing imo. Right now we have the strategic elements of a war in place (deckbuilding and gathering vault intel). Allowing teams to pick and choose who fights what battle would add that second crucial component that is a part of every war, the tactical planning. In reality if you are fighting a battle against multiple opponents, it's common for different factions to try and prevent one from becoming too powerful. You have to balance throwing all your top resources against a powerful foe against using them on matchups you feel they could be the difference between winning or losing. In the end, getting a better chance at a win is better than trying to prevent someone else from getting one.
If you really want to discourage "teaming up" a small rule tweak could be that upgraded cards used in General/Lt decks can be salvaged as upgraded cards that can be used by any member of the winning team. This way throwing you General/Lt at a strong team only makes sense if you think you will win, otherwise you run the risk of making that team even stronger. So for example Higs uses Fractix on me and I win. My team could salvage 4 Minor Phoenix and they would stay in the Vault as MP's that any member could use at any time in the future. The benefits here are some teams will be more hesitant to use their General/Lt against elements they view as very powerful, but if the perceived weaker elements beat them the added potential upgraded cards can help close the gap between them and the their stronger enemies. This might be too significant of a change however but something to consider.
Or you can even set up something like:
Regular Player defeats General: Can salvage up to 6 of the already upgraded cards from the deck
Regular Player defeats Lt: Can salvage up to 3 of the already upgraded cards from the deck
Lt defeats General: Can salvage up to 3 of the already upgraded cards from the deck
** Any other wins result in the normal salvage of only unupped cards