Other sports that allow more than 2 entries in a sport: Track & field, cross country, golf, and I believe tennis, swimming & diving, gymnastics too name a few. Mostly other sports with individual competition.
At some weights for instance two 250 plus pounders that don't have five pound weight differentials around their weights, it is almost impossible to move your weight enough to go to another weight class. And we need to get away from excessive weight cutting which kills wrestling's image with the public and can have adverse health consequences. I have seen a number of quality kids not wrestle varsity in recent years due to this lack of opportunity. Should two shot putters from the same team who can both throw 60 ft not have the opportunity to compete at State?
I am not opposed to your idea about maybe reducing to three classes instead of four in the method you are proposing.