That would still be the same coin flip as with the selection of 2vs2 and would end in an even worse position for the loser of the coin flip.
If your opponent chooses a mech that has the advantage against yours then you would want to switch your mechs.
But now seeing you switch to that mech allows your opponent to choose his 2nd mech specifically to be good against your 2nd mech.
With that you would be forced to switch back to your 1st mech which the opponent will follow accordingly by switching back to his 1st mech.
Now you have to fight against mechs that you are guaranteed to be disadvantaged to.
In the 2vs2 selection both players have to choose both mechs without knowing the opponent’s mechs that will be used.
As such both players have a 50% chance for both mechs choosen to get an advantage.
But in your setup you have that 50% chance for your 1st mech only and then are guaranteed to be disadvantaged if you lost that coin flip because the opponent can choose his 2nd mech AFTER you have choosen your 2nd mech.