Why do we need a pull-up resistor if we can just make a short to the power source?
In your drawing, the pull-up resistor does pull pin 2 towards Vcc, but allows a trigger input to pull pin 2 low in order to trigger the 555.  If you connected pin 2 directly to Vcc, you could never trigger the 555.

In general, pull-up and pull-down resistors are used to hold a signal line at a default (often "inactive") state, but allow the line to be pulled to an active state by other circuits when required.

If you want a signal to be held to Vcc or Gnd at all times, you can usually make a direct connection to Vcc or GND.  (There have been logic families where a direct connection of an input to Vcc is not recommended, so a pull-up resistor should be used there, even if the pin will never be pulled low.)