Really ??? 
… Seriously ??? 
You expect a player to give up playing while they volunteer time to police the chat @ tables?? Thats asking a hell-of-a-lot from people… Alot more than say a paid employee, which still is asking alot and possibly is counterproductive…
As for having mods incognito, thats a fair question. I dont necessarilly alter my chat at the table ( “Sassy-ness” ), yet the fact a mod is there is ALWAYS in the back of my mind, so yes it does kinda alter behaviour. On the flip-side, its nice to see mods on tables so we know they are out there should we need them. I will say Replay can do better in having Mods available when need’d.
Just as in “Undercover Boss” ( even tho I am now thinking its all just advertizing the brands ) , Boss’s have seen that a disconnect between mgmt and customers/employees is counterproductive is most situations. I expect staff to compete for things for the simple fact that : Only by compete’n can they detect possible unfairness or areas that need tweak’n/improvement. When you only make the rules, then don’t play by them , you don’t see unintended consequences of certain rules/chgs.
I would be in favor of a modified “incognito” for mods at tables, where they appear normal… but if a situation arrises then they can toggle thier “purple-ness” so players instantly know… holy crap, that really is a mod… Recently I need’d a mod, and one wasn’t avail, so we need more mods, and we can’t ask players to doante time, if they are not eligible for promos/leaderboards.