I think that there is a time and place for the chip shot. Personally, I don't trust it very much. I only use the chip if my lie is perfect and I'm either on the fringe or on the lip of the fairway, and the cup is within 8 yards or so.
While the pitch is more manageable to strike, stopping it is sometimes a problem. A pitch, as everyone knows, tends to roll quite a bit depending upon the green conditions and geometry. I pitch in only limited circumstances that are far too narrow to try to describe here.
So how do I handle the short game around the greens? The flop shot, of course! The flop shot is, in my opinion, easily the most forgiving shot that the golfer has available. It gets up high quickly, strikes well even in second cut rough, lands very softly, and rolls in a slow, predictable manner. But it has limitations, as all shots do. I don't ever ever trust it out of the sand, for instance - never. However if you find yourself on the fringe with a long putt over uneven terrain, in the fairway just off the green, or in the rough close to the green, the flop shot is your ticket.
You have to hit this shot differently than any other shot. For starters, it is only used with a small wedge (I use either my 56 degree or 60 degree with equal confidence). Use FULL backspin, and pull it. When I say pull it, I mean use the first mark LEFT of center as your "ding" line. The reason is that a flop shot is made with the club face very open. Using the first mark left of center as the aim point for your click reliably compensates for this.
Another consideration is the direction the ball will take after it lands. Due to the factors just mentioned, a ball tends to roll to the right after landing. This is usually quite noticeable and once you get a feel for it, you can use it to deadly advantage.
So consider practicing this shot. If you are like me, once you master the nuances you will think of it first whenever you are just off the green or on the fringe with a long, snaking putt in front of you.