The storyline of the original three movies which I saw as a kid, (now IV, V, and VI) have a completely different story if taken separately from I,II II,III III. The republicRepublic still stands for Anakin he goes through the whole transformation from jediJedi to sithSith, originally trained by the actual quote unquote school"school" for jedisJedi with an actual teacher, as the Republic falls and the Empire is born.
The reason, if there is one, for the discrepancy that you point out is that Luke is constantly being shocked into getting better at using the forceForce. Think of the idea of if someone is pointing a gun (or a laser gun) at you, you will be forced to get better quicker.: saving the princess huge experience, learning Vader is his father, losing his hand, getting a lightsaber, flying in a space ship, destroying a death starDeath Star single-handedly. Remember he was a dirt farmer for all appearancesappearances' sake. Anakin was building droids and racing pods!
Alternative ideas may stem from the idea of balance in the Star Wars universe., the balance between light and dark, and good and evil. I think they made it clear there aren't many good jedi'sJedi at that point, and by the time the final battle with the Emperor and Vader takes place, both Yoda and Obi-wan have died and are with him in spirit. Is it possible that he, without much control over it, has a boatload of power? (which can buy you a lot in a fight, especially when it involves the force.Force)?