I think giving the ability to change decks between matches is really needed, to make it more strategic, by a sideboard, of this way:
First you make a deck.
After the first fight, you get the option to change add up to 3 cards from your deck, you can take out as many as you want.
You repeat that, until you or your opponent has won
After that, the winner gets to chose 6 cards from all the cards his opponent used, so his original deck, and the up to 4*3 cards he used later
The lose has to discard 24 cards
The rest gets added to the vault.
This makes your original deck more important, as it is now, but you can still react on you opponents deck, by adding more pillars/control/creatures/etc.
There is something in favour of using a sideboard too: You can get a completly different deck the next turn, from mono to duo, or back, from a duo to another duo, etc.
Using sideboards would also solve another problem, the problem of the bigger decks, because you can give every player 45 cards which he can use to fight with.
so:
Sideboard= deck changing between matches
Only 3 cards = only acclimating on your opponent, which can help already a lot.