What's the advantage compared to large commercial aircraft that don't stall their wings on landing?
A full stall landing is generally a bad idea for everyday flying, regardless whether you're in a Piper Tomahawk or a 747. The slightest error can lead to stalling well above the runway surface, resulting in a drop that can injure the pilot and passengers, damage landing gear, and in some cases even damage the fuselage structure or main wing spar. Even if perfectly executed, it also leaves you in a very bad position if, for some reason, you need to go around -- you've given away all your energy and have to get enough of it back to not only keep flying, but climb, and do it before you run out of runway or obstacle clearance.
A full stall landing is a special STOL technique, and most pilots require intentional retraining to do it, because the approach is flown much more slowly than normal -- normal approach speed, what pilots are trained to do routinely, has a significant margin above stall for safety (because a stall at low altitude, even in absence of a spin, is likely to result in a potentially fatal crash).
Even a "three-point" landing in a conventional gear aircraft isn't usually flown as a full stall -- the airplane can assume the three-point attitude and still be below stall AoA, assuming the descent angle isn't too steep.
When you land you want to be as slow as possible to minimize ground roll, maintain control, and reduce stress on the landing gear. Ideally, you will stall the airplane a few inches above the ground. If you stall the airplane a few feet above the ground you will “drop in” and have a hard landing. Ask me how I know.
If you are much above stalling speed you have more energy to dissipate on the landing roll. This could be a problem if there is a strong crosswind or a short runway. One of the things the FAA stresses is to always fly a stabilized approach and landing—even if you don’t need to for a particular runway. You may not need the precision on a 6,000' long 150' wide runway but it comes in handy when you land at a 2,500' long 50' wide grass strip.
As the FAA explains in the Airplane Flying Handbook:
The touchdown is the gentle settling of the airplane onto the landing surface. The round out and touchdown are normally made with the engine idling and the airplane at minimum controllable airspeed so that the airplane touches down on the main gear at approximately stalling speed. As the airplane settles, the proper landing attitude is attained by application of whatever back-elevator pressure is necessary.
Edit: Wolfgang Langewiesche and others disagree with Zeiss Ikon. Talking about taildraggers, “The exact length of the landing gear legs depends therefore on just how much the designer expects the pilot to slow the ship up before setting it down. In most airplanes, the designer goes pretty near the limit in this respect; he expects the pilot to slow the ship up to actual stalling speed before letting it touch the ground, and he proportions his landing gear accordingly.”
Michael Love in his book Better Takeoffs and Landings, writes about tailwheel three-point landings. “In the textbook full-stall landing, the airplane touches down on the main gear and the tailwheel at the same time. The airplane should be fully stalled as it touches down…”
He writes that “Tricycle-gear aircraft should be landed in a nose-high position, touching down on the main landing gear, with the nosegear off the ground. Figure 4-6 shows a typical tricycle-gear airplane correctly executing a full-stall landing.…The aircraft is approaching a full-stall just as it touches down.”
I have taken instruction from instructors certified by the Bonanza Society under the Beechcraft Pilot Proficiency Program. They teach that you should aim for full-stall, full-flaps landings every time.