It isn't like Southpark: Stick of Truth where the kids all agree to take turns in battle. In DnD everyone is acting at the same time and that time is a span of 6 seconds, not 6 seconds divided by the number of people in battle.
What you are describing is people gaining super speed relative to the number of people in battle. For example, in a 1 v 1 battle, you are saying that each person spends 3 seconds on his action, then waits 3 seconds for the other guy to do his thing. Yet in a 10,000 v 10,000 warzone, that same guy gains superspeed enough to make that same action in 0.0003 seconds. The question then becomes, in the 1 v 1 situation, what if he is a Chaotic being that chooses to ignore the gentleman's agreement that was compelling him to wait the 3 seconds for his enemy to attack and attacks at his full potential? If he can take an action in 0.0003 seconds, then he could take 20,000 actions in the same round that the Lawful guy (that is still respecting the gentleman's agreement) takes only 1