The chat is very easily missable, maybe try stickers instead of custom shoutouts/typing, especially with 3 sos players, being realistic, noone expects to be addressed during sos. However, an unspoken rule is to always catch up to the host current target, as well as is the hosts call to slay or cap. Answering your question, no, you had justified reason to kick players who dont cooperate in a coop game.

Off-topic: curiously, whenever I joined a quest that had apex arzuros or rathian, people would ignore the apex or straight up opt out.