Microsoft delivered firmware updates in July 2018 that caused display and driver problems for some owners of Surface Pro 4 devices. This has been an ongoing support issue and only recently recognized by Microsoft as something that needs to be addressed by something other than just another bug fix.
According to WindowsUnited, Microsoft support is now aware of the problem and is swapping entire devices when customers approach support with the issue.
Unfortunately, the support staff could not tell me anything about the technical background of the bug (could have been that Microsoft has made a corresponding handout to). Only that it lies on the firmware update from July and Microsoft finds no solution for it.
My Surface Pro 4 replacement is already on its way to me. It is of course a nonsense that a Surface Pro after an official firmware update can be used only limited.
Original Microsoft support thread: Surface Pro 4 – broken after 26th July update