It could be security-related, but not the same security you and I think of when discussing browser security. Incognito mode prevents cookies, localStorage, and history from being written to the company-owned computer's hard drive. It therefore makes forensic investigation of things like sabotage, ex-filtration, pornography, threats, etc more difficult, especially for organizations with limited resources. In some cases, an investigation into an incident is basically having the IT guy poke around the hard drive; if that's the case, incognito makes such an examination less fruitful.
While i'm sure a lot of experts on here will scoff and bring up infosec topics like custom certs, screen viewing software, nannyware, keycatchers and the like, many small businesses are lucky to get their systems up and running, while security is an incident-prompted afterthought. With a powerful overseer, incognito does little, but against mom and pop, it can be very effective.
As far was why edge gets the capability and chrome doesn't, I would guess that it's easier to administer/deploy a customized chrome than edge. If you still want to use incognito, consider using a portable app copy of a browser, which isn't bound by your companies IT restrictions.