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
@themetman Good to hear your solution. May be helpful for others in the future.
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