Wouldn't it be much simpler - and we'd no doubt avoid all these disputes and misunderstandings - if players just holed out? It's not as if conceding putts is speeding up the game. They were taking 3 hours to play 9 holes 
The sight of a professional golfer looking for a nod or listening out for an "it's ok / that's good" when faced with a 6-15 inch putt is just silly. If you're clearly hoping your opponent gives you a putt, isn't that a very good reason for your opponent not to concede the putt?
Has there been a situation where a played picked up a ball after hearing "it's ok" and it turned out that it was someone in the crowd that said it, rather than the opponent? If it hasn't happened yet, it's bound to happen at some stage. (EDIT: I just read this may have actually happended in the Pettersen/Lee incident)
These situations are just open to too many misunderstandings. The Suzann Pettersen incident was another example where not conceding a putt (which was her right) got her in hot water.
There are good reasons unrelated to pace of play for conceding putts in match play, where, unlike stroke play, you are "protecting the field".
Suppose in a four ball that Player A is away, and A's partner is only a foot or two from the hole but would be standing in an opponent's line. A is putting for birdie; the partner is putting for par, and the sensible team strategy would be to have A's partner putt first to make par and allow a free run for A's birdie putt. Both players on Team B have birdie putts; how they putt them will depend on whether or not A makes his/her putt. In this case, conceding A's partner's putt is good strategy to keep footprints out of their line.
Another example that happens commonly is when a player who is out of the hole has a putt along a similar line as their partner's putt, which DOES matter. Their opponents don't want the player who is out of the hole to show their partner the line, so they concede the meaningless putt, which means that player is NOT allowed to putt the ball. That concession really, really matters, especially at the professional level where players learn a ton about line and speed from watching a similar putt.
Those two situations come up all the time in match play; I'm sure there are others, but you get the idea. And when to concede and when not to concede putts are things that make match play hugely entertaining to play and watch.