The phase of voltage across a resistor in a RC circuit when the frequency of input tends to zero
You write

then the voltage across the resistor is in phase with the input voltage

But this is not correct. Simply because the right-hand-side vi-vc is real does not imply that the left-hand-side vr is real if vi-vc is zero.
For w approaching 0 the capacitor voltage is in phase with the input voltage, and VR approaches 0 with angle approaching +90deg. This is calculated from the voltage divider equation.
Below are simplified plots for Z=-j/w (C=1,R=1), and H(w) for the resistor.