if you don't make allowance for the temperature you are still protected.
Not quite.
Assume the temperature is say -31 (ISA-46).
You are happily flying down the presented VPA and have it pegged exactly in the middle - not even 1ft of deviation. You are not worried that the VPA has reduced from 3 to 2.5 degrees because you know that the obstacle surface will have reduced also and will be OK.
However, When you are on the VPA and the altimeter says you are at 350ft, what is the true altitude of the aircraft?
Without bothering to work it out, it is a lot lower than 350ft and if that was your DA then you are actually well below it unlesss you have made the appropriate temperature correction.
So to sumarise - as the temperature drops the VPA decreases. As the VPA decreases, the obstacle limitation surface also decreases. There will be a limit of how shallow an approach you can make and this limit will be reached as the temperature lowers.
So the minimum temperature ensures that the VPA does not get too shallow.
A separate issue is that unless the DA is corrected for cold temperature then when DA is indicated on the altimeter the aircraft will actually be well below the DA............a long way below it at -31C!!.
To satisfy yourself use -31C and sea level. The VPA will be 2.5deg. With a DA of 350ft - how high will the aircraft actually be and at that level how far away from the threshold?
So you are lower than you think you are and closer to the threshold - do you really what to be there when you have to go missed on a limiting missed approach procedure?
Ask yourself - If you are flying an ILS with a 2.5deg glideslope (provides the required obstacle clearance) and the temperature is -31 - would you not bother to do a temperature correction to the DA simply because you know that the glideslope keeps you clear of obstacles?
Regards,
DFC