Yes this thread is indeed about a variation on the standard initiative system for D&D 5e and so the observations about the Monk are valid. In 5e, fighters, at least strength based ones, are usually ahead in AC and hit points compared to monks. I didn't think about this before but this system would definitely make skirmishing harder to pull off, although not impossible. If the Monk rolled really well on initiative and the opponent rolled poorly, there is still a chance the Monk could pull off all his actions before the other guy can act.

But to be honest, I've played monks before and the skirmishing tactic was hard to make work even with the standard system. You really need the mobile feat to make it work and most times you still didn't have enough movement to move in, attack, and move out without retaliation on the next turn or round.