When you do missions you will notice that the whole world does not load some places are blocked so even if you were allowed to stay in the area it would be restricted. It would be best to let the player have an option to pick the next mission or pick explore mode.
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It's true that the missions are 'instanced' so for example, ppl who are not in your fireteam can't follow you into the mission (they seem to just... evaporate :). But once the mission is over, the 'instance' can simple end and re-opens the game world for exploration again.