Conceptual Question About Circular Polarizer

I have a wide angle Tokina 11-16 and I have a good quality circular polarizer attached to it. Aren't the effects of the CP essentially the same as not using one but rather editing saturation, vibrance & clarity when editing the image. Trying to understand the real advantage of using a CP. Thank You.

A polarizer attenuates reflections from non-metallic surfaces like water. Post-processing can't do that.

A polarizer also darkens skies, and that can be simulated in post.

Polarizing filters are absolutely effective for their purpose which is to handle reflective surfaces, be it water, skin, foliage, etc. Very effective and what they do cannot be reproduced in post-processing without insane dynamic range. The effects on saturation and all that, sure, that can be mimiced in post. But the removal of reflections cannot be done in post.

Here's an example of polarizer off / on and its direct intended effect that cannot be reproduced in post:

No polarizer:

Terrible glare/reflections that clips data and makes it harder to expose properly.

IMAGE LINK: https://flic.kr/p/qTsZ​YM

IMAGE LINK: https://flic.kr/p/qTxv​BC

IMAGE LINK: https://flic.kr/p/zMva​rh

A CPL will reduce reflections from most all surfaces to a degree. It will make colors richer and skies darker.

I've found that many people that try using one don't realize that you have to orient it to the sun. Years ago the CPLs had a little mark on them that is meant to point toward the sun. My newer B&W does not have this so you need to find out witch way to point it and mark it. Simply take it outside and roll it between your fingers while looking at most anything. You'll see certain surfaces change intensity, darken or the reflections will disappear. That is when the polarizer is properly oriented.

A polarizer passes light that possesses a certain plane of polarization while blocking light not in that plane.

When light is reflected, it's plane of polarization tends to be parallel to the reflecting surface, so reflections can be greatly reduced with a polarizer. Aside from the uses mentioned above, it can also be used to reduce reflections from glass, such a photographing an object inside a glass case- my personal experience is that it can make a great deal of difference.

Likewise, scattered light (which is what we see in the sky) is also polarized- this polarization is proportional to cos**2(theta) where theta is the angle from the incident light. This is why a wide-angle photograph (whether from a wide-angle lens, or a stitched image) shows the banding mentioned above; we are seeing light scattered from a different angle relative to the sun. I didn't know about the mark mentioned by @saea501, but that might help with the banding. It also suggests that shooting towards, or away, from the sun with a polarizer will have minimal effects.

It is interesting (or annoying) sometimes to have polarized light (from the sky or reflected from something) impinge on something that has stress, such as a tempered car window or an airplane window while using a polarizer. You can get interesting (or annoying) patterns or colors.

These effects can't be replicated on software; polarizers are one of the few filters which can't be duplicated in software.

Even at 24mm I've had the dreaded uneven polarisation effect when my subject matter is not exactly at 90° with respect to the sun. I wouldn't recommend using a polariser for darkening skies on landscape images shot with a wide angle. I prefer to use ND grads for that.