In terms of the debate: Eventually you'll need to have policies in place around ownership of work produced, and while there's nothing preventing an employee from copying files to a personal device, having everything they work on stored on hardware owned by the company makes it significantly easier for the company to enforce those policies.
If you supply standardised equipment (a particular model, operating system, etc) it will also help for the setup of any new employee, and any interoperability that may be required. Everyone will get the same; troubleshooting requires a focused spectrum of knowledge and experience rather than knowing how to troubleshoot Windows, Mac, Bootcamp, Ubuntu, CentOS, on desktops or laptops.