Omg! I freaking LOVE this idea! The details in my mind are a bit different, (Toggle raid/nightfall/strike icon that shows beside name), but yes, definitely a great idea!
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I definitely like the idea of using icons to identify which events a guardian is looking to run, I think this would work best in the Roster menu. It could work off the same menu system. Guardians running around in the social area could have the simple visual identifier like the name color change, and individual icons identifying which events they want to run by their names in the roster menu.