Why do we have capacitors at IC supply pins

In analog/digital circuit, we always see capacitors being connected from supply pins to circuit ground, but why?

From my perspective, the two primary reasons for those caps are:

Reason #1:

Connection from supply to IC has impedance - those caps (placed near the IC) will supply most of fast current demand which gives less voltage fluctuation on supply pin when supply current flows

Reason #2:

The supplies  are not ideal, regardless of them being a battery or switch mode supply, there is always internal impedance/resistance, and those capacitors will make sure the IC "see" low impedance supplies across the frequency of its bandwidth (remember that capacitor impedance drops as frequency increase)