Can a resistor on its own do anything
Almost everything we have in electronics is useless on its own. What good is a light bulb by itself? With no power source you can't light it. Even with a power source, it is still not all that helpful with out a switch.

Even the more complex things, like a microcontroller, are pretty useless on there own. Even if you have a power source there isn't much purpose of them unless they are connected to other things.

As for focusing on the resistor itself, there are things that it can be useful for when combined with a power source. For example, creating heat. If your goal is to create heat with a very simple component, using a resistor with a power source is a very simple way of doing it.