Well, they're just a tool. They don't do anything magical, but their use at the right time can make an enormous difference on some planes. Less so in others.
I've been getting my head wrapped around the F4U-1A, and at first I couldn't see the big deal about the flaps, where everybody raved about them. I prefer to keep that plane fast anyways for the most part. Then the other night I wound up making a bad move and getting into a turnfight with a spit of some kind, Co-E, on the deck starting at 130-150mph. I dropped a couple or 3 notches of flaps as the spit started into a series of straight loops. I don't know why either, but it seemed to make him happy. We weren't deviating at all, just straight (well as close to straight as a couple mediocre pile-its can fly them in here) vertical loops.
It just so happened I was low on fuel. Not sure how low, but probably below 1/4 tank on the main, with my wing tanks burned down to 1/4 each. In that series of loops under WEP, I was riding the stall horn pretty much all the way around once my nose got above the horizon, but I was constantly gaining on the guy. They let me get over the top, and shortened my turning radius at the bottom. 2 1/2 loops or so later, I pulled lead and killed him. This is with dead straight, nose to tail, me running on WEP with 2 or 3 notches of flaps. It felt like I could continue doing that maneuver until WEP ran out, I wasn't gradually slowing down.
I did an off-the-cuff couple of tests later in the evening, with more fuel, and couldn't get the same result with that maneuver. It seems to me it was the fuel weight that made the difference. In my testing I'd stall out on the way up on the second loop.
I've also had plenty of situations where a guy was trying to force the overshoot and my flaps allowed me to stay behind him by slowing me down.
They're not even remotely close to necessary, but I do believe that situationally, and between a pair of pilots of equal skill (whether they be top-shelf or mediocre guys that are still trying to use ACM) their proper use can make a difference.
Wiley.