Some tabs have a plate(metal, leather, etc) which gives you that shelf, or wall, for string indexing. Obviously the Olympic archers prefer the metal tabs. So, I'm wondering, what's the advantage to having this edge for string indexing?

I can see where it might help a string Walker, but other than that, I don't see the advantage.

I've tried tabs with metal plates, but I haven't liked them.  Tabs such as the SafariTuff have a stiff leather shelf that feels better in my hand than the metal plate.  The purpose is to give you consistent tab placement shot after shot.  I see no downside to having consistent tab placement, and since it feels good in my hand, I use it.  I doubt that it matters that much, but every little bit helps.

I use a metal Yost tab and a Jenkins Safari Tuff tab. I string walk and I can shoot either well.

I agree McDave. I just don't see a disadvantage of using a tab that doesn't have a "lip"

I'm just looking to learn, if there is something to learn

One reason when I shot a tab I used/use the Black Widow tab. I bought one of those AAE metal tabs. I just could not get used to the metal. I did like all the adjustments but was never comfortable with it.