To rephrase - a short is really a very low resistance, so low that your power supply can not source enough current to develop a steady voltage and as a consequence the output of your power supply drops to almost 0V, doing some nasty stuff on the way - resetting/turning off everything on board (nothing can work on 0V) AND letting all the current that it can source to run thru the switch. Probably causing something to heat up and evaporate.
When there is a reasonably big resistance pull up resistor, you don't have this problem - the power supply can easily source enough current to develop a rated voltage across it. In this case you'll get 0V at the bottom of pullup resistor when the switch is closed, but power supply will still provide proper regulation and no high current will flow thru the switch. (well almost 0V, the switch has some small resistance that was causing problems in previous paragraph, but it's so small when compared to pullup resistance, that it's negligable in this case)
You don't leave the input floating as it's effectively a gate of a FET that is really just a small capacitor that can easily charge up or discharge from stray electric fields that are always present around, turning the input on or off. I.e. you would not be able to determine when the switch is really off.
I'm sure you can find far better explanations on pullups in this site written by true greybeards, just look around.