Because with a resistive / capacitive parallel load, the total current is the vector sum of pure resistive current (current in phase with voltage) and pure capacitive current (current 90 degree lead from voltage). If the two components are Ir and Ic then the lead angle is atan2(Ic,Ir) which is 0 for Ic = 0, Ir > 0, and pi/2 = 90 degrees for Ir = 0, Ic > 0. So you are always between 0 and 90 degrees lead for RC parallel loads. It's not like the lead angle is proportional to the capacitance.

The gyrator thing is a lot less useful than it looks in theory (I have never encountered one in an application).

Jason is right that you can only get +/-90 phase shift from one capacitor/inductor. On the other hand you can easily make a chain by combining several such RC/RL networks and get a phase shift of any angle (just be aware that in a passive network the stages influence each other so calculating the required circuit may not be an easy task).

The real problem is that you cannot change the frequency dependency of a capacitor so you can always easily discriminate between them by changing the input signal frequency.

Simply increasing passive capacitance can only cause the current phase angle to asymptotically approach the limit of leading by 90 degrees. However, in op-amp circuits they can be used to eliminate inductors, but this has more to do with the topology of the feedback circuit than any innate ability to shift phase.