Is there any way to allow team members to raise the issue on GitHub by simply sending the details to some email address, like how FogBugz allows it?
Currently it's not possible.
I have confirmed with GitHub staff by sending email. Currently you can only reply to existing email notification in order to post the comments on the issue. For new issue you have to raise manually on the GitHub site under your repo or use other custom plugins. Though they are considering it as a feature request.
Further, if anyone is interested in reporting issue on GitHub or have some support query, they can send email to
firstname.lastname@example.org. They are very responsive, I got reply within 5 mins.
Our team at FundersClub built a simple tool to let anyone in the team who does spend too much time in GitHub easily create GitHub issues via email. We were originally using it internally at FundersClub to make sure our engineering team can capture all product feedback from the rest of the team with the least friction possible. We just made it available to anyone for free.
You can find it at https://fire.fundersclub.com.