I think that turn-based play is grossly underestimated, and the existence of this mode of playing deserves more promotion; here is the place to collect advantages and inconveniences linked to TBP.
Several negative reactions often come back when mentioning TBP:
I also have the impression that TBP really becomes interesting when one can play lot's of games simultaneously: if you have only a few games running, chances are that in most of them you are waiting for the opponent to move, and thus TBP will be boring; but if you have several ongoing games - especially with opponents from distant timezones - at almost any moment of the day you have the occasion to move.
I'm not sure to what extent the inherent lapses of concentration (because one will wander off into other games, come back later and have forgotten the context of a particular game) are bad for one's play in general. What I notice is that after seevral years of play, I can recognise an ongoing game amid 50 or 60 for example, and also remember where trouble spots lie. This was impossible when I started playing (on DGS, btw).