Why build it with a 5-20 and attach a 5-15 adapter? Doesn't make sense really, but maybe I am being thick headed.
At first glance, it does seem a bit silly. Since every 5-20 (20A 120V) receptacle accepts a 5-15 plug, why not just put a 5-15 plug on the cord to begin with?
In order to get the 20A rating that is advertised, you can't put a 15A-rated plug on the cord. Even if there is no difference in the electrical properties of the 15A and 20A plugs, and the 15A plug *could* handle 20A of current continuously, the orientation of the prongs determines the rating in the eyes of regulatory, testing, inspection, and standards agencies. Hence the adapter.
As it is, the receptacles on the cordset are rated at only 15A. But when summed together, the total loads could exceed 15A.
In my opinion, every extension cord that is rated lower than the circuit it can connect to should be equipped with a fuse or circuit breaker (as they are in Europe). Many fires have started because someone overloaded a 16AWG extension cord plugged into a 20A circuit -- and the properly sized and functioning circuit breaker never tripped.