I'm loving the explorer mode.
Fantastic idea and hope it opens into other things for solo players.
I wouldn't have the loot the same as for playing dungeons (maybe raids in the future) properly (with the difficulties as they would be normally), maybe give old season exotics and legendaries or something?
Anyway, I don't care about the loot, I'm just really enjoying the gameplay option.
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I think adding it to future dungeons on release would be fine. I don't think it should count for solo run triumphs though. And I don't think the exotic should drop from it. If they stay, they should be there to get you ready for the normal mode dungeon.