Without R present, R will have an infinite value, so the C*R high pass circuit will have an infinite time constant. When turned on, the capacitor charge will be zero. Without R there will be no way of charging C to the voltage needed for AC coupling or DC level conversion. A high pass filter requires both C and R be present. Without R, you may as well replace C with a wire link.
Op-amps are imperfect and have an input bias current. That requires bias current cancellation, or some way to prevent integration of bias charge in C. Ibias*R decides the maximum acceptable value of R and hence the physical size of C needed for a particular signal frequency.
Very high impedance AC coupled amplifiers used in the biological sciences often require a “de-block” state in which the input capacitors are charged to bring their voltages close to that needed for the common mode input range of the amplifier. Once “de-blocked” the very high impedance inputs place minimal loading on the biological system. The shields on the input cables are “bootstrapped” from buffer amplifier outputs to neutralise the cable capacitance.