I will preface my comments by saying that I have only a few hours in the 172, and it's been a long time. Having said that. here's a few cents worth. Being a philosopher, I like knowing the why of things. The 172 is a four place airplane, typically used as a training tool with only a pilot, and CFI, both sitting in front. Since this is a trike configuration, the elevator controls are someone more limited in size, deflection, and effectiveness than the comparable 170 model. with only two aboard, and no baggage it's probable that the CG is at or near the forward limit of the plane. Now, it'll fly and land just fine with this load, but think of the job the elevator is trying to do, in landing configuration, with full flaps.
In this configuration, the plane will have a pretty serious nose down tendency. so, the answer is to trim for that, and remove the pressure from the elevator. By trimming, we remove effective and actual elevator area from the moveable surface(trim tab deflects down, elevator deflects up, all is well). The full flaps also brings the plane to a lower speed which will also contribute to less elevator effectiveness overall.
So, although I can see the reasons for having full flaps down on all landings, I can also see a reason to limit the flap travel to 20deg when landing with only two aboard in a 4 place aircraft. Now, if one were to have 4 folks, and a bit of baggage, then the full flaps will produce the low speeds desired, without the concomitant poorer elevator control or deflection. I find this is very relevant in the short fuselage Bonanza, with 30deg of flaps and no one in back. I typically land with 10-20deg with one or two aboard.
this is the sole reason the school in DFW doesn't let the primary students land with flaps. The owner of the school has suffered several prop strikes due to nose first, or porposed landings, and considers the cost of gear/brake repair acceptable over the cost of prop/engine/nose gear repairs shoud a student bash up the front of the plane. Not that it's right, or even defensible, but I'm just the messenger.
Let the slings and arrows begin!