whatever photo the Host asks for seems to become rarer than normally. but HOLY does it feel overdone! especially when he asks for a jogger.
Viewing post in Snapshot! (NSFW edition) comments
Having a task by the Host or not has no influence on the appearance of characters. More importantly: the Host task are entirely optional ways to earn a bit more money in the early game. They are unimportant later on.
As for jogger spawning: this is currently much lower than in the patreon version and will be increased in the next update.