Yeah, Sided Initiative is a pretty common go-to for many PBP games. It's not DH specific at all.
Like, a game of D&D that uses normal initiative might go something like: Player 1, Player 5, Enemy 3, Enemy 1, Player 2, Enemy 2, etc.
Then you wait half a day for Player 1 to go, another half a day for Player 5 to go. You get Enemy 3 and 1 done pretty quick. Player 2 takes another half day to reply, you're busy that day so you don't get Enemy 2 finished until the end of Day 2, and that's just half the round.
Where Sided Initiative for D&D is just, "I wrote their turn. Everyone try to get their turn in before I check back in tomorrow." Then you resolve their turns in the order they posted them, unless one of your players specifically says "Oh, I want to cast Bless before Bob and Jane go!"