Well, here is mine:
Please be reminded that feeding a 1* troop gives 40 experience points, a 2* troop gives 90 experience points, a 3* troop gives 200 experience points, and a 4* troop gives 400 experience points. One of the problems leveling your main troops is the cost of food. The higher the level of the troops, the more expensive and costly it is, food-wise.
Back then, prior to the release of the Hero Academy, players only have the maps, quests, events, gem offers and in-game Shop as sources of feeder troops, among others. While the maps and quests may provide 1* and 2* troops, rare troops are not easily and readily obtained as getting them may often involve gems, or Epic Troop Tokens. Summoning from the troop portal however gives the summoner a 10% chance of an epic troop.
Please understand that training troops at levels 2, 4, and 6 of the Hero Academy is a nice new feature and addition to the game. They can serve as a recruits storage, as well as iron storage, which was previously non-existent. Of course, by reason that they are obtained from the HA at the cost of iron and recruits (and food for researching the function), they may take some time to spew a recruit. I agree that getting 3* troops after 2.5 days of training at the HA is quite to long, while the training camp level 20 produces mostly 3* heroes, and a chance of 4* and 5* heroes, in only 2 days. But skipping them at the cost of gems is ill-advised. Of course, you cannot compare the skipping cost and the summoning cost. I think it is a feature to avoid being abused by players.
But I still believe SG will be fixing Hero Academy soon. Like what they did to the Alchemy Lab. But instead of waiting for that to happen, I might as well churn the gears in there. At least its productive.