I'd say using a 13/16" in 3/8" drive with any real torque is probably overstressing the drive tool. Perhaps a breaker bar would be OK, but I wouldn't want to put a good ratchet on that.
To me, I place a limit on the socket size to double the drive size. (If I need a size larger, I go to the next drive size).
So, a 1/4" ratchet shouldn't be really pushed past 1/2". I know there are 5/8" sockets for 1/4" drive but I can't see where I'd be limited to 1/4" drive.
With 3/8" - 3/4" would be as big as I go.
Though with 1/2" drive and up I think you could extend that upper limit a bit and be OK, as by then the steel knuckle is getting pretty thick and it survives torture better. Especially with a cheater bar.
Just my opinion.