The choice of wing-low or crabbed depends very much on the type of aircraft. As Paco says, a B737 needs to be landed crabbed because of its underslung wings.
But try flying something small and light with high wings - say a Piper Cub - crabbed, and as soon as you kick it straight the wind will pick it up and you'll loose the centre-line - wing-low is the only way to land that type of aircraft in anything other than very light cross-winds.
Most training aircraft - C172 included - can be landed using either method. The crab method is the one I prefer, purely because it can handle higher cross-winds than wing-low. I normally teach that to all my students. But if a student is having trouble with this method, I will teach them the wing-low method, and I'm quite happy for them to use that if they find it easier, because it is very much personal preference.
As for cross-wind limits, the 15kt "limit" on the C172 is
not a limit, and it
explicitly states this in the manual, in the definitions in Section 1:
Demonstrated Crosswind Velocity is the velocity of the crosswind component for which adequate control of the airplane during takeoff and landing was actually demonstrated during certification tests. The value shown is not considered to be limiting.
(I've added the italics.) However, having said that, I would be very surprised at any school letting solo students fly with a crosswind of the kind you are describing.....
FFF
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