Not trying to tell anyone how to suck eggs but thought this might be interesting for some.
My progression has been from a Canon 10D (no rude comments please) with all the nice lenses to a series of point and shoots and now I have a Sony RX100 III.
For my type of photography (mainly travel) it is just great.
I was at a beach location with strong sunlight and I then remembered that I actually carry a polarising filter. Just a cheapie and not circular.
Also camera doesn't have any adapter threads for filters.
Just remember that you can just hold the filter up to the scene, get the correct orientation that you want and just hold it in front of the lens.
Simple, cheap and effective. I carry mine around in a converted hotel shoeshine shell.
It is the only filter that I carry as I think all the others can be duplicated in software.
Sorry not interetsed in discussing circ vs linear etc just letting you know that there are ways to do things differently.