The purpose of the breaker is to
- protect the wire
- protect the appliance
The reason the wire is first priority, it is typically more difficult/expensive to replace and likely has a higher probability of starting a fire.
Extension cords are typically down rate because of the abuse they see over time. Higher probability of one or more strands breaking.
If you built in some kind of a fuse/breaker box near the male end of the cord that had 2 - 20A breakers, then a 10 gauge cord would be protected when plugged into a 240V 30/50A circuit. It might not meet the letter of the law, but it certainly meets the spirit.
But they probably should be !
The NEC is a bit odd on 15A/20A circuits is residential buildings. No requirement for 20A receptacle, even though 20A circuit are required is several residential location.
(Of course, when has anyone seen a 120V home appliance that draw over 15RLA and has a 5-20 plug on it ?)
Technically, yes. This is part of the oddity of the code.
You can plug a 20A appliance into a lamp extension cord (rated at less than 15A) and into a 20A receptacle and circuit. In that case the extension cord is the fuse ! 