Need a clarification about capacitors. Why would current flow in a C-R circuit if there is a capacitor? Won't it behave like an open switch?

Because charge is capacitance times voltage, an uncharged capacitor has no voltage across it.

For a resistor and uncharged capacitor in series, all the voltage is across the resistor, and thus a current flows.

When the capacitor has charged up to the supply voltage, there is no voltage across the resistor, and thus no current flows.

CURRENT ONLY FLOWS DURING CAPACITOR IN CHARGING CYCLE AND THEN FULLY STOP.