I can get why this is done, so that some GEN recordings won’t be “spoiled” when IA publishes them. Though, that also implies that people who join at the start of a MP session might not be recorded.
I know IA publishes a few custom MP sessions on YT, with stuff a normal player can’t do. However, some people do have the hardware can host pretty effortlessly. If it’s possible, the GEN coding can/should allow MP sessions to record a mission if the player joins in at the start (like as soon as the MP session is published) or within the first level.