Pull Requests are a great code review tool. On projects where code review is enforced for regulatory requirements (SOX, PCI etc...) it would be handy if the "master" branch would only accept modifications via pull requests and not pushes. This would enforce the code review process and provide evidence to the compliance officer of the regulatory requirements being met.
This would only apply to a single branch like "master" or configured branch, and users with write permissions can continue to push to other branches in the repository. This is a very basic form of Branch ACL (#3276) but with a narrow scope providing lots of value within the corporate environment.