I would honestly prefer a socket style system.
aka ALL legendarys AND exotic armours would come with a "raid socket"
whenever you are awarded a raid armour peice the armor stats would identical with any other legendary of the same tier, but in addition you would ALSO receive a raid token, which can be placed in any armour peice of the same type with a slot, for example if you were playing kinfs fall and
Darkhollow Treads dropped, before you would get them and barring the changing perks you would have the additional perk of RUN FOR YOUR LIFE.
now instead they would NOT have the run for your life perk and you would receive Darkhollow Treads minus the run for your life and a "run for your life token"
place the token in the Darkhollow Treads and boom they function exactly like they did before...OR place the token in your Days of Iron Boots boots and now THEY function like darkhallow treads, for their raid perk, but you get to keep your own armor look. furthermore you can actually combine this system with yours, make teh tokens a set, and you receive a set bonus for each token currently equipped. but now you can make ANY armor your raid set.
sorry this is horribly explained, if someone with better eloquinces is willing to give it a shot at what i'm trying to explain, please, go ahead.
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Applying raid perks to any ordinary piece of armor? Never. The perks need to be tied to the gear or otherwise there's no incentive to run the raid. Loot drops being replaced with an arbitrary "token" is thematically boring. Why should vendor trash inherit the ability to grant you a speed boost while in another dimension? That makes no sense - Now gear that is fashioned from the scraps of Hive wizards and thralls SHOULD have that type of ability. The reason why raid gear makes sense is that it is thematically tied to its activity: SIVA weapons with SIVA perks found in the SIVA raid, for example. Some mundane chest piece bought in the tower SHOULD be mundane - it's ordinary and offers nothing special.
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you can only get the raid token FROM DOING THE RAID. aka you have to get the legendary peice it would normally be on FIRST before you even get the token. the way it would work is raid perks would be a separate item from the raid armour piece that would drop alongside said armour peice, now you can go and place that item in your raid piece you just got, OR place it in any appropriate piece of gear you already have. so long as it has a raid token slot. the incentive to run the raid is still there. furthermore, this balanced a GAMEPLAY reason and the players own preference for aesthetics and the way THEIR gaurdian looks, instead of shoehorning players to look the exact same for the raids.