While Public missions are fun, a lot of players (including myself) tend to go into missions in Solo mode for various reasons. One reason I've come across lately is to stay longer in a survival mission without having to go through a host migration.
I suggest an alternative Mission Mode that ensures the player is the host ahead of time, adds 5 or 10 seconds to the countdown to help them still find a party, and otherwise plays like a Public mission. This way they may end up Solo after all or someone may join and leave early but it wouldn't impact their game.