I have a young daughter that can randomly desire my attention when playing story missions. An actual pause mechanic would be useful if I wasn't playing with others even a timed pause during missions like sports games do would be appreciated.
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That wouldn't work because Destiny is an always-online game. Even when you're doing story missions you're still in an online game where other people can randomly show up. The best thing for you to do is get to a safe place to hide.