Praying Shacharis and Mariv (morning and evening prayers) is listed as one of the things "sheodom oychel peiroisehem..." (A person eats of the fruit in this world but principle is left to be enjoyed in the next world). Yet it's Shacharis and Mincha (afternoon prayers) that are obligated in the Torah. So why not mention Mincha but Mariv instead?
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It seems to be that it is not necessarily praying Shachris and Maariv, but rather "hashkamas beis hamidrash" at those times. The verse is thus not calling out davening but synagogue attendance.
Since Mincha is often prayed "on the go" or as an interruption to the work day, it would stand to reason that it is more common to attend communal prayers in the morning and the evening.
Nothing to do with prayer. "Going to Torah study in the morning and evening", i.e. before and after work.
I'm having problems with the premise of the question: There is authority to say that Mincha is the most important service. Rabbi Chelbo at Berachos 6b states that Mincha was most important because Elijah's prayer was only answered with a Mincha offering (see I Kings 18:36-37). Today, Rabbi Berel Wein, argues that Mincha is "perhaps the most important and meaningful prayer service of the day" precisely because it is inconvenient, must be done in a narrow window of time, and interrupts the work day. Because it comes in the middle of the work day, it "is an oasis of spiritual time in a tough workday." Shachris and Maariv, however, are possible to be prayed outside of difficult time constraints.
One could argue that Maariv is least in importance because it doesn't have a direct connection to the daily Tamid offering. Rashi to Berachos 26b. But see Rambam Hil. Tef. 1:6 and the Tur (Orach Chaim 235). But it and Shachris are tied to the time-bound mitzvot of saying the Shema.
So, I really don't think you can play favorites and say one service is more or less important than the others.