We've been huge fans of anytime dining (called by different names on different lines) since the first time we encountered it. We never wait for a table, but I suspect that may be because we're in the top tier of the frequent sailor clubs on a number of lines, and I think that shows up on the computer when we give our room number. In any event, we're always taken at once to a table of whatever size our group happens to be that night.
We place no value whatever on having the same table and the same waiter every night. I'm perfectly capable of saying "iced tea please" each evening and I get no thrill about the waiter knowing that ahead of time. And of course, we consider set meal times a liability, not a benefit.
The flexibility of eating whenever the spirit moves you just can't be beat. Not just the obvious benefit, but the additional one of being able to eat with friends you've just met and hit it off with (a great many of whom--no surprise--also choose anytime dining).
It's clear that more and more people are going this route, and I imagine that, just like dress codes, eventually the forced seating times will be marginalized and may disappear.