I was pondering this a while ago and wanted to understand the outcome in relation to novices-higher handicappers.
In order to mimic a novice-higher handicapper, I borrowed some left handed clubs (I play right handed) and attempted to play left handed putts, hybrids, chips and pitches from closely mown areas, from manicured 2" rough and from gunge onto both flattish and domed greens.
The outcome - significantly better results with the putter/hybrid every time from the closely mown area, even a bad putt would reach and stay on the green. Poor results from the manicured 2", often taking 2 shots to get onto the green, frequently 3 shots if heavily contoured. From the gunge, awful, just awful, could barely get the ball out in 2-3-4 shots.
To me, and others may disagree, closely mown is preferable provided a machine can cut it, a kind of if you can cut it, cut it low approach.
However, I would also suggest that some grass types do not allow the ball to roll unless the grass is cut very, very short, and I guess this has maintenance issues, and maintenance issues also need to form part of the debate.
atb