However, I do not consider this to be a drawback, since every psalm is set in common metre so that tunes are interchangeable.
Agreed. Instead of a drawback, I believe it is a bonus because it gives a person complete control to use whatever (common meter) tune they want with any of the 150 Psalms. With other psalters that assign a tune for each selection, you need to know that tune (or read music) in order to sing that psalm.
Sort of struck me as funny...you could sing every psalm to "Amazing Grace" if you wanted to. Me being a person of routine, I would make a great worship leader...

"...*Ahem*...we will now sing Psalm 4...it goes just like Psalm 3, 2, and 1 that we did a little while ago..."