Indeed I think that it in order to get to the level of prayer where shorter davening is meaningful and transcendent, you need to experience marathons of time spent in shul and hours flipping pages in piyyutim and prayers.
On Shabbat, in reading the story (Bamidbar 12:13) of Miriam and Aaron's concern over Moshe's marital situation, I was struck again by the simplicity of Moshe's prayer to heal Miraim's leprosy.
The authority and power of Moshe's simple prayer stems from his individual greatness and recognized mastery and knowledge of Gd. He is also known to be a sincere mediator and one that he can pray at great length (see Mt. Sinai 40 days and 40 nights for those doubting). I think this signifies the key quality for a brief and powerful prayer.
For a more modern example, one small throwaway comment from the President of the United States on a specific topic could send the stock markets or political issues through the roof - whereas my own personal pontifications about the S&P, Bonds, or the Supreme Court will not make the waves at my family dinner table. The power is in the authority of position and communal value placed in the leader. Otherwise any student could rise up and say, "get well soon" without moving the congregation.
Thus, we are moved by Moshe's elegant prayer knowing that he can also daven the long prayer. My personal conclusion, we need to teach the long form of prayer even though the students probably prefer the short form. I will enjoy try to enjoy and explore more this paradox.