Duel tournament.

The banning process works like this:
Out of 24 available heroes, each player takes turns banning one hero until only 12 remain (each player bans 6 heroes).

Am I understanding correctly that the opponents share a common list of heroes? And that 12 heroes remain for both of them?
Wouldn't it be better to do it the old way in tournaments, where each player bans 12 heroes from the other, and each player is left with 12 heroes? Because if there are only 12 heroes for both, the player who chooses first has an advantage, as they can take the strongest hero.