You can put a 50 amp range receptacle on a circuit anywhere from 40 to 50 amps. There are also exceptions for things like welders.
15 and 20 amp duplex receptacles have the same pass-through current, only the plastic faceplate and prong configuration are different.
You cannot put a 15 amp Simplex receptacle as the only receptacle on a 20 amp circuit, and the same rule applies for a 20 amp Simplex receptacle on a 15a circuit.
If there is more than one outlet, like a 15 amp duplex receptacle, you can put them on a 20 amp circuit.
I, too, have seen many 15 amp receptacles burn up on a 20 amp circuit, however most of them were due to back wiring / backstabbed wires, loose side screws, or a receptacle that is so wore out that does not make adequate contact with the prongs on the plug going to the device.
And yes, the 5 - 20r receptacles tend to be a little more expensive, and since they are internally identical to the 15 amp receptacles (and cannot be used on a 15 amp circuit), most contractors are going to use the 15 amp receptacles everywhere.
The extra price and not needing to use a 5-20 r is why I say that most of them in a residential setting are installed by non electricians.
To that end, if you cross connect is not in the panel, it is likely inside of a switch box that can handle two circuits in, and at least a switch leg and a circuit out. In my experience, a double fed circuit is never cross connected inside of a single gang box.(eta: in an older home, it could be inside of a ceiling light box)