It's not exactly the same thing, but a neat science trick is to take a $20.00 bill and soak it in isopropyl rubbing alcohol. Then light it on fire. It will burn pretty and blue, but the bill will come through unscathed. The water in the solution soaks into the paper and protects it from burning and the alcohol just burns on the surface. Try it. With a $1.00 bill if you think I'm joking
I'm not sure of the concentration in most sanitizers but it may be that the inert gel ingredients form a barrier between whatever you are trying to start burning and the burning alcohol. Could be the reason it doesn't work so well.
In my survival kit I have a plastic tube stuffed with petroleum jelly soaked cotton balls. I also have 3 different methods for starting a fire. Lighter, matches, magnesium block/striker. I also have hand sanitizer but I've never tried to get it to burn.
The cotton balls with petroleum jelly are also useful for sealing small cuts, treating chapped lips or dry cracked skin exposed to the elements. It will also insulate your nose/ears/face and prevent frostbite if you don't have sufficient cloth to cover them.