thron: Thank you for the instructions. I did not know there were problems in this area until I saw this thread.
When I saw it, I decided to try connecting my Lumia 640 LTE, which I had updated to Windows 10 months ago, to my Windows 10 AU system. This had earlier worked with the 640 on Windows Phone 8.1, with a Windows 8.1 PC, but I had no occasion to connect the 640 to a PC since then.
When I connected it, the Lumia 640 LTE alternately appeared and disappeared from the list of devices under "Computer." Further, within Device Manager, the 640 LTE alternated from being reported as "working properly" to not being so. This alternation of state occurred over matters of seconds. Further, this occurred in both USB 3.0 and USB 2.0 ports.
I disconnected the 640 and uninstalled all hidden devices for it from within Device Manager, as you recommended in your post, and then rebooted.
After reboot, I reconnected the 640. When connected to a USB 3.0 port, it was then recognized solidly. However, when connected to a USB 2.0 port, it was still not recognized solidly; i.e., it sometimes disappeared and then reappeared a few seconds later.
I also connected the 640 to a USB 2.0 port on a Windows 7 system. [I had not connected it before to that computer.] The 640 was solidly recognized.
Hopefully, what appears to be driver problems will eventually get sorted out. In the meantime, I will only use a USB 3.0 port if I wish to access the 640 from my Windows 10 AU system. Or, alternatively, I can access the 640 from a USB 2.0 port on the Windows 7 system.
(I also notice that, on the Windows 10 AU system, if I minimize the Explorer window showing the phone, it pops up after a short while. This indicates to me that it is likely that some event has occurred, even when the 640 is connected to a USB 3.0 port.)
All of this apparently points to driver problems, although it is not clear which driver is flaky.
If uninstalling the drivers does not solve the problem for the OP, as a temporary workaround I would recommend trying different USB ports and/or different PC systems.