From the following graph I understand it is because they reach the voltage and the current reach their maximum values at the same time on the resistor, but I don't understand why this should be that way. What is the intuition behind this?
Why do you think the phase should be different? Which should lag or lead?
Ideal resistors have no lag. If you apply a voltage, the proportional, steady-state current appears immediately. As the voltage changes, the current changes alongside.
All real circuit elements have some non-zero inductance that would make the current deviate from this ideal. But for a small circuit with wires and resistors, the inductance and deviation is usually tiny enough to be ignored.
here is why, intuitively.
Take the case of a mechanical resistor (dynamic friction in a mechanical system). if you increase the speed at which you are working against friction, the system responds immediately without any lagging. Similarly, if you decrease that speed, the system also responds immediately: this is because the resistance contains no inertance and no compliance.
If the system contained inertance (mass), then you would need to apply a force to change the velocity- so the force occurs before the velocity change. If the system contained compliance (springiness) then you would need to develop a displacement before the force could be transmitted into the system to change the velocity. Both of these effects introduce phase shifts between the forcing function and the system response.
Those phase shifts are absent when the system consists of a pure resistance that contains no inertance and no compliance.