I'm noticing two things when converting RGB files to CMYK and I'm wondering if I'm doing something wrong or if the software is doing something wrong.

First, when I assign a CMYK profile using Image > Convert Image Colour Space, the image appearance does not change. Yet soft proofing with the same profile achieves the correct results.

Second, when I save a JPG as CMYK it blurs the image. I'm not referring to colour changes, nor compression issues, but a very significant anti-aliasing of the entire image as if I'd applied a blur filter. I can mitigate this to an extent using Quality and Sub-sampling but this results in a file some 30X the size which is still less defined than the original. Exporting to PSD is fine.

EDITed to add; the blurring only occurs on reloading the image after Save.

Software it is, then.