Do not use “Chemical proof”
It’s not a good color profile for CMYK conversion.
If you absolutely want to manage CMYK conversion by yourself, use the color profile expected by the printer (your print shop must be able to tell you which one to use)
After, why the soft proofing doesn’t work on your side it’s hard to say, tested on my side I can see difference on document with and without softproofing (with “Chemical proof”) but it should be easier to see it on a document with saturated colors like this one: