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
Still trying to understand: you have this view and an exposed form on it, right. And you have two independent taxonomy terms and try to filter by them? Or is this a hierarchal...
Parent items won't show on Leaflet Widget.
Sorry. It is a taxonomy term.
Parent items won't show on Leaflet Widget.
Hi geoma, hm... I'm not quite sure, what "parent" means in that context. Is it a taxonomy term? Or a related node type? The map will only show geo data from the field...
Parent items won't show on Leaflet Widget.