If Ash/Misty got a cold, what would the other do?
Depends. If Ash is in the field and Misty is at her gym, then Ash wouldn't know or care if Misty had a cold, and Brock would tend to Ash's cold. If they were traveling together, chances are they would either try and cure the cold or act like they did when Brock got sick. Except that Brock would probably be the one doing everything.