I’d been recently caught off guard by the lack of sharpness on the long end of my 16-300mm VC lens so I performed a brief test with and without my frequently used 67mm circular polarizing filter. The drop off in sharpness is completely the fault of the filter. At 16mm with my polarizing filter mounted I do get a very sharp image, but at 300mm with the polarizing filter the photos become very hazy. There is no noticeable loss of sharpness from wide to telephoto end without the filter. The filter used is a 67mm slim Zomei filter.
Remember to always conduct sharpness tests on lenses without filters, and if you want to test the sharpness of the filters themselves you must do so in controlled exposures.
*Note that none of these photos are intended to be flattering shots, these are uncorrected jpegs in harsh backlighting.