Generally when you select public matchmaking it means you don't want to play alone. It's not great if the party doesn't fill up or people drop out, especially for mission types like interception where having 4 people is a big advantage.
My suggestion is that anytime the party count is below 4, the empty party slots are filled in with a random Tenno specter until someone joins to fill in that slot. This would only apply in public matchmaking; invite or friends only implies some degree of party coordination, and solo is self-explanatory. Or this could be a new matchmaking type for opt-in pu
I imagine this working like the Index where the specters don't prevent other players from joining, they're there as a stopgap until a real person joins the squad and replaces the specter.