A student is taught to go-around because it is safer than trying to fix a screwed up landing
I suggest that is a wide generalisation. You first have to define a "screwed up landing."
Before first solo it is vital that a student be instructed on and demonstrate the ability to safely go around in the landing configuration from final approach and from a bounced landing. However a go-around from a high prolonged hold off at close to stall speed, has its own risks; particularly with a low hour pre-solo student.
A go around in a full flap configuration at a very low airspeed can be very unforgiving unless yaw is immediately prevented as full power takes place. Nose attitude must adjusted appropriately. A poorly controlled yaw at slow speed in the landing configuration, if not prevented, can quickly lead to a full power incipient spin in the landing configuration. This can prove fatal at low altitude. Practice until competent is vital.
Under these conditions it is generally safer to land ahead by applying partial power, at the same time adjusting the nose attitude in order to "cushion" the bounce or high hold off; assuming adequate runway or landing area is still available.
It is up to the instructor to first demonstrate these two manoeuvres to the student. In turn, before first solo, the student must demonstrate he is competent to carry out both types recoveries competently and safely.
On the same subject the following advice is published in the Boeing 737 Flight Crew Training Manual under the heading of Bounced Landing recovery.
Quote:
"If the airplane should bounce, hold or re-establish a normal landing attitude and add thrust as necessary to control the rate of decent. When a high hard bounce occurs, initiate a go-around. Apply go-around thrust and use normal go-around procedures." Unquote.
In other words, not much basic difference really, between what is taught in a Cessna and a 737, n'est ce pas?