What do we need the op amp for in this current-to-voltage converter?
Your op-amp is a vital clog in the wheel in this circuit. Since the op-amp has infinite resistance, the current I entirely flows to the alternate path through the resistor R. Note that since the + end of the op-amp is at ground and because of the infinite gain of the op-amp, the - end is also held to ground. So the drop across the resistor is V = IR. So effectively, the output of the op-amp will be held at V = IR as the output is connected between the point V which is the other end of the resistor and ground. So, it is the characteristics of the op-amp which are enabling the functionality of a current to voltage converter here.