No reason you can't make an optional choice in exotic quests like "kill x number of guardians in crucible OR kill x number of bosses/minibosses in pve modes" for example. That way you cater to both types of players and noone gets pissed off by having to play modes they don't want to.
Edit #2: Changed title to include PVE as well because apparently people just read titles now and don't bother to read the actual post content before going full keyboard warrior. ;)
EDIT: Man some of you are getting mad butthurt over this.
1) It's just a suggestion that would benefit both types of players, pve and pvp. yes it says pvp in the title but I say in my post there should be options for BOTH. Learn to read more than a title before going full keyboard warrior.
2) Again this is just a suggestion and noone is "crying" about anything. Generally if you have that attitude, you're just projecting your own attitude towards things.
https://en.wikipedia.org/wiki/Psychological_projection
3) It's just a game. Some of you are taking this waaaay too seriously. Maybe take a break and go do something else for a while if you're this invested in a video game, and that's coming from someone who has played them for probably longer than most of you have been alive.
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Dude, don't put a link to a wiki article you don't understand in your post.