Whoever replies first usually gets the conversation, and everything AFTER that first reply used to be unchased: a proposal could go out and be met with silence forever. A couple who meant to reply and forgot looks exactly like a couple who chose somebody else, and only one of those is worth a nudge.
Chases go out on their own. You see them in the event's history, so you always know what was sent in your name.
Every recipe can be switched off individually on the Automations screen. Turn one off if your own follow-up habit is better than ours — the worst outcome is you and the app both chasing the same person.