I believe there are good musical reasons also for the problem of men not singing. Hymn settings are usually in four voices, and the melody (the hymn tune) is often NOT suitable for many men to sing! Few men are tenors, while most are baritones, and few are basses. Singing the tune an octave down doesn't work well; and when a tune is begun in the baritone and the melody ascends beyond the singer's range, he needs to drop an octave or sing in falsetto. This, too, does not work well musically. It also leads to voice strain and a sore throat for the untrained.
In the Scottish a capella tradition, the split-leaf psalters come in two editions: staff notation and solfege. The idea behind the solfege edition is that every body can sing the part that is in the natural range of their voice using "movable do" solfege. Actually, singing in "movable do" solfege (the historically correct solfege that preceded the counter-intuitive and artificial French system of fixed do) works very well if one can read staff notation, too. I recommend the Kodály Method for learning this; it's VERY easy. Another historical method that used to be popular is the tonic sol-fa method.
In the previous churches I used to belong to that practised exclusive psalmody, many would actually take the time to learn and memorize their parts. The resulting sound is beautiful and edifying, and well worth the effort.
This of course is only the musical aspect of the problem. There are other issues, too...

In this was manifested the love of God toward us, because that God sent his only begotten Son into the world, that we might live through him.