I suppose it depends on the context a little bit, and the severity of the error. For something like a 404 page it might be overkill to have a feedback form field — however on more serious error pages (like an order failing to go through on a store) it makes sense to have a method to communicate any concerns to the company you’re dealing with. On 404 pages something like a link to your support page or the contact details of the company may suffice.

Hope that helps!