Replace order of initiative by a lot

One of the most tedious and non-dynamic parts of combat is tracking the order of the initiative in combat. As well as its predictability from round to round.

WoC once tried to fix it by rerolling initiative orders each round, which only made fights even less dynamic.

However what if we go a step further? What if instead of rolling initiative we would draw it by the lot?

For that: put PC & monster's name in a box. At the start of the round draw one name and put it aside — it's theirs turn. Once they finish draw the next name, and repeat until there is no more in the box and round ended. At the end of the round put all names back in the box.

On the plus side, it removes part of the combat routine, creating a permanent source of tension, as now you don't know when an enemy pulls the trick, you only know that with each drawn name this moment grows closer as well as a moment of your turn. This uncertainty forces players to try a variety of strategies within one combat, mixing and fixing them.

On the negative side, making long-term combat plans become difficult and there is a possibility that someone will get a double turn or will not get a chance to act for almost two rounds. Though such occurrences can be fixed with a couple of simple rules — let's say the last turn in the round is the most desirable one as it gives an advantage on one roll of your choice.

So what do you think? Can it work better than just ordering? Has anyone already tried something like that? Is there are some obvious problems I'm missing?