Being the owner of a home with a well and a water softener I forgot to fill, I got to experience what hard water does to your shave.
It affects it a lot more than I thought it would. The biggest problem is the soap scum. It makes your face and razor "sticky". It feels as if the lather is drying out, but it's not.
Soft water provides a much superior shave. So much so, that it would be a reason to buy a softener if you don't have one or use distilled water to lather and rinse.