Next time you forget to remove the lens cap from your camera,
try the PhotoShop "remove lens cap" effect--it works wonders!
To belabor what was said by AndyH: the image sensor doesn't
detect polarization, so that information is gone. PhotoShop does
not yet support "clairvoyance mode".
(Sorry to sound so snarky, but the "fix it in PhotoSlop" mentality is
one of my pet peeves. Also, I can remember when news guys
had to haul around heavy Graflex press cameras, Nikon F2s, etc.
One little filter is nothing.)
Perhaps it would be easier if you carried your filters in a belt pouch?
Nice ones are available in various sizes for about $10:
https://www.bhphotovideo.com/c/buy/Filter-Pouches-Cases/ci/238/N/4026728364?origSearch=filter+pouchIt would be great if there was a more convenient way to swap filters,
but there really isn't. Holders like Cokin and Lee don't really save
any time unless you are using mutliple filters. Flip-up filter holders
are available for microscopes and optical benches, but not for cameras,
so far as I know.
Some materials become polarizing only in an electric current, so
it might be possible to build a polarizer filter that could be switched
on and off--but it would probably be
very expensive.
Some news photographers used to carry two cameras, often one
with a normal lens and one with wide angle lens. Some locations
are too dirty, dusty or wet to fool with changing lenes or filters.
In other cases there might not be time.
So I suppose you could carry two cameras: one with a polarizer filter
and one without. But that seems like a lot more trouble and expense
than a filter pouch!