Why is ISA Standard pressure 1013.2 not used for contour charts instead of QFF?
Maps and charts show true elevation, meaning tape measure altitude from the sea level. The way the mapmakers and chartmakers measure elevation has changed over time. Currently, I think GPS is prevalent. The way GPS computes elevation is depend on the WGS84 Geoid earth model. This modes surface does not coincide with actual sea level but GPS takes that into account. And today in most aeronautic related industries WGS84 is becoming a standart, which also includes maps and charts.

On the other hand altimeter provides height using pressure of air. QNH and QFF are the altimeter settings used to adjust for non-standard pressure and temperature, respectively. QNH is always provided to pilots and is the most prevalent. I have never heard that the QFF is used or requested by pilots. 

As I said QNH setting only corrects for non standard pressures. It really assumes ISA temperature, 15C. So as you asked what happens if the temperature is not standard. Well someone needs to compensate for that and make correction. 

Colder than ISA temperatures needs to be corrected for minimum enroute altitudes and obstacle clearances. Because the aircraft will be at lower true altitude than what altimeter shows, at colder temperatures. As for hot days, it’s less risky because aircraft’s true altitude will be higher than what is shown on altimeter. Only example comes to my mind is when you’re shooting an approach that has decision altitude kind of minimums. Since the aircraft will be higher than true altitude you may end up going around during real minimum IFR situations. However you will be on the safe side at hot temperatures, in terms of obstacle clearances. 

As mentioned in that article; correcting minimum sector altitudes (MSA) and minimum vectoring altitudes for non-standard temperatures are ATC’s responsibility. In other cases, such as doing a published approach, it’s pilot’s responsibility. 

That same article provides an excel at the end to use on the ground. Also some pilot operating handbooks provide charts to apply for altitude adjustments for non-standard temperatures. One technique for flight planning is to find the correction for the coldest temperature for  the day and apply that to whole flight. But that applies only to GA type flights really. 

Not only that,  but also, there is this phenomenon called geopotential altitude. It implies that 1 altimeter-measured-feet at sea level is not equal to 1 altimeter-measured-feet say at 30,000 feet. And that’s because gravity is not constant as we climb. So the actual true elevation of the obstacle will always be slightly higher than what you see on your altimeter even when you’re side by side. However it’s really a small difference (less than 1%) and not a big factor at low altitudes where obstacles mostly live. [wp reference]