This is what I see from my drops experience. With "real" RNG I should be closer to the middle of the Gaussian distribution graph with any class.
Yes, but what are you distributing over? My point was that you can't expect the RNG to normally distribute items per class because the items themselves are not all designed to be class-specific.
Think about any rare 1h weapon - it could be used by any class and the RNG could select from all the available stats in a way that makes it "classless" (e.g. avg dmg, weapon dmg%, life steal, open socket, chd). That's a "good" example that could potentially be used by any class. Then there are the meaningless examples, which we are all familiar with, that are useless to any class (the best I've found was a quadfecta resistance ring with a socket - TY RNG). So, given most items in the game can be used by more than one class and given the typically large number of stats available to the RNG for any given item, how could you reasonably expect 20% chance to find a drop relevant to the class you are currently playing let alone any class for that matter? The design of the items (i.e. the available stats and the "classless" nature of most items) guarantee this.
So, technically speaking, the class relevance of an item is not a continuous variable to begin with because there are many "classless" items in the game, hence, it is unreasonable to expect a normal distribution. Therefore, it makes no sense to expect 20% of your item drops to be relevant to the class you are playing. One also has to remember that there are subjective elements to "class relevance" based on build and playstyle anyway (e.g. although perfect trifecta dex gloves would be godly for any monk, it might be terrible for a TR monk to have an IAS roll).
The only way something like this can be achieved is to redesign the items to ensure relevant stats for each and every item are available to the RNG. In all likelihood this will actually have to be developed as parameters to the RNG: e.g. if player = barb, give a heavier weight to strength. This and other possibilities is what the D3 developers are calling "itemisation" - the RNG will give you more relevant drops (while also reducing the number of drops). This is partly to offset the reliance on AH. See link in previous post.
So, your observations are right, your expectations are a little unrealistic regarding class relevant drops, but the itemisation patch is likely to address your concerns. Until then, you gotta play the AH or craft.