Why did Bungie remove private matches? I know many people who beat the storyline, maxed out their light levels, mastered all of the raids and finished nearly everything that the game offered. The only reason they still played D1 was to be able to get on with 1-11 other friends and mess around with the many game modes and maps available.
Private matches give guardians the opportunity to play crucible in a way that just isn't possible when they are put up with random people. They can play without a certain few weapons and with a certain set of rules that adds extra excitement to the game.
It is also a good way to practice for trials and come up with strategies as a team. Private matches help teams bond and helps friendships grow. I have a number of friends who I came to know better, and eventually led into my clan, from playing private matches.
With the new clan system and importance in Destiny 2, private matches could be implemented into the rewards system. For example, you could get a clan engram from Hawthorne if a certain amount of private match completions has been meet, or if everyone, or half (which seems to easy to do) in the fireteam is in the clan, or both. It could have a potential for adding on to the clan.
Private matches played as huge part in the Destiny 1 experience, and I can't see why they can't do the same for Destiny 2.
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Or take it one step further with custom games