Where does one commonly find NEMA 5-20 plugs/receptables being used nowadays as opposed to NEMA 5-15 plugs/receptacles wired with 12 gauge Romex wiring fed through 20 amp circuit breakers?
You'll find them in Kitchens, Dining Rooms, Garages, workshops and other locations where 20 amp service is installed.
It's typical "homeowner" engineering to use a 15 amp receptacle on 20 amp rated circuits. Everything in the circuit supports a 20 amp load except the receptacle. I see the failing of this mostly in workshops or garages where an owner has installed 20 amp circuits but loads are equivalent or greater.
You would do well by replacing a duplex 15 amp receptacle for exterior connection with 5-20p or a 20 amp GFCI receptacle since GFCI is required for exterior receptacles.