Join in Progress works in call of duty because of loadouts. It doesn't matter when you start a match because you can pick and choose what weapon you have. If you get thrown into a match that's 4 minutes in, in Halo, you're almost guaranteed that the other team has BR's, has secured some of the power weapons.
Additionally, Halo has a greater focus on team play and map control. Does it matter where you join in Call of Duty? No. You spawn and run around with short kill times, respawn. Whereas in Halo, if you are coming into the match, the other team could have secured the key areas of the map already and once they're entrenched, it's hard to change it coming in.
If someone in CoD is holed up in a key building, I can spawn with some kind of explosive load out or a sniper loadout and take him out from far away, but how can I do that in Halo with just an AR/pistol?
I may sound confusing but I was really thinking about this. It's just so vastly different that it just doesn't work in Halo. Especially if we're talking competitively. I'd ideally like to start a Warzone match from the start as well. I'd hate to be put into blowouts.