Trials can still exist, but there needs to be the addition of a weekly skill based endgame for PvP in Destiny 2. Once a month IB isn't good enough. The quality of the rewards should be the same as any end game rewards, and maybe the cosmetic appeal of the rewards changes based on skill tier.
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I can see where you are coming from, but I do not think it should be solely skill based, because, honestly, ToO is solely skill/meta based, and it drives a majority of people nuts. I think it should have some skill elements, but merit and trying should be the focused on aspect. If you normally go with a 1.5 KD type thing and you get a .5, you get nothing, but get a 3.0 and you get a better light/rarer item. This, however, would more than likely see a lot of people dropping their KD, ELO, etc, then coming in and destroying everybody for the loot. Honestly though, Destiny was marketed as a PvE game with a small influence from PvP. Now it is a PvP game with small influence from PvE.