How would the game break if one used a "single initiative" system?

[n00b]

Complete n00b trying to teach myself Melee here.

I was wondering the reasoning behind the double initiative system: Both sides move based on the initiative roll, and then individuals act based on Dex order.

HOW would the game break if one used a "single initiative" system instead? That is, one in which combatants move and immediately act. For the sake of discussion, the order could be

a) Determined by a die roll (side initiative),
b) Determined by Dex (individual initiative), or
c) A combination of the two, such as 1d6+DEX.

I am asking HOW the game would break rather than WHETHER it would break because I presume that there has to be a deep reason why it works the way it does. But having read the rules and tried a bit of arena self-play, I cannot see any obvious reason!

(Edit: Notice I am asking about basic Melee rather than Melee+Wizard or full-blown TFT. Answers about the full system are welcome, but I'd like to understand how Melee works on its own first.)