Originally, I did just that with my service. The problem is when you need simple information like "What browser and version are you using" when someone says something "isn't working". Capturing User Agent during form submission takes an otherwise painful step out: asking a non-technical person to find out what version of Internet Explorer they are running. There are still people who think "The Internet" is "the Blue E on my computer". Similarly adding required fields like "What's your site's address" when you run a multi-site service. All valuable things to have specified so that you can answer any questions with the first response rather than having to ask a pile of followup questions when customers don't provide enough info.
With a general purpose email, you don't get that.