It doesn't necessarily seem intuitive (to me at least) to keep an assortment of your personal effects folded up in a leather pouch that then goes inside your pocket, especially before business cards and credit cards existed. About when, and how did wallets become standard?
I'm not really sure what you mean by "standard". Are you asking when they gained their current form? Or when wallets became popular?
The word "pocket" and "wallet" used to mean the same thing, a bag that was typically worn hanging from a belt.
Pouches have been in use for a long time. Otzi had one.