Because everything adds weight and everything costs money......but mainly because it’s not required.
There are also not enough occurrences to warrant it.
we’re not talking engines running at or past their design parameters with rapidly changing loads....like race car engines that are only expected to last one race before rebuilding anyway.
To the original poster ‘double_barrel’ :
Examiners will and should take a very dim view of applicants making up their own procedures.
You shouldn’t. Neither should your instructor.
Unless it’s in a manual from the manufacturer or a publication from an official aviation source it’s a technique and as such subject to opinion.
At this stage of the game you lack the insight and experience to tell correct from tribal law and superstition.
Think about this for a moment:
A C172 does not have complicated electric, hydraulic, pneumatic or fuel systems.
No multiple hydraulic pumps increasing pressures to 3000 psi while heating hydraulic fluid to boiling points.
In a light GA airplane you can have three types of fires: electrical, fuel or oil.
Fuel off and mixture cutoff will starve a fire quickly.
Oil you cannot shut off but if you have a big enough leak for the oil to combust on a hot exhaust then you’re out of oil pretty quickly.
The cowling will contain most of the flames and if it does burn through the cowling you have 65-70mph ( best glide) wind for a fire to deal with.
Again, there is no system like high pressure fuel pumps or hydraulic high pressure pumps to sustain a fire.
Keep in mind where the fuel is in a light GA aircraft....the wings.
You’re probably more likely to get an electrical fire in your wings because of bad wiring then an uncontained engine fire that would I require you to sideslip the flames to where you hold the fuel.
i know that’s what your instructor told you.
They're not always right.