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
Very possibly, I am looking at it now... Sorry I will be travelling away on that date. I will register, so I can look back
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Great news Francis. I'm glad I could help. Any chance we will see you at the upcoming Backdrop Live?
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Well your second Idea seems to have done the trick! So Simple!!!!! I can use this all over the place!!! Big Hug, and Thanks a Million, @yorkshirepudding !!!
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