There are several advantages to flying at high altitude, like decreased drag, faster true airspeed, and if you're pointed the right direction, higher tailwinds.
The first question you need to answer in a power-off landing scenario is this: do you want to maximize the distance you can glide, or do you want to maximize the amount of time you can stay aloft?
Contaminated fuel on the ground can lead to serious problems in the air. Here's an example of pilots that sumped their fuel and still had a contamination-related engine failure.
You're flying an ILS through icing conditions and your airspeed suddenly begins decreasing. Your pitot tube is covered in ice. What would you do? Here's what happened to this pilot.