Description of the need
I suspect that most people who enable the core Contact form do so in order to allow visitors to contact them, without needing to provide their email address publicly. As such, I also believe that most emails recieved through the contact form have nothing to do with feedback about the website itself (that seems like a very specific use-case).
Proposed solution
I therefore propose renaming the default Contact form category from "Website feedback" to something like "Website enquiry", or just "Enquiry". To me this seems more generic and a better default option.
Alternatives that have been considered
Users can always just edit the default category themselves (I personally have to do that all the time).
Additional information

Recent comments
well @herb I cannot believe it, but the webform module was there in modules on the disc, but missing in the listed modules, so I delete the module folder, and downloaded it again. Then...
My Webform Worksheets have disappeared
The only thing I can think of is to make sure Webform module is enabled and that the content type that needs to contain the webforms has Webform enabled for it. Edit the content type and make...
My Webform Worksheets have disappeared
@yorkshirepudding, In the end I fixed it by deleting the config/active folder contents, copying the config/staging/ files into config/active, importing the database again and clearing the caches...
Importing the staged config throws an error: another field with the same name already exists