If you want to connect, I would use the RDC. RDC will allow you to connect your local drives to the remote machine so you can copy files from the remote machine to the local machine.
For tech support, as others have said, I would use remote assistance to shadow the users desktop. Yes, it is cumbersome to do this since they have to send you an invite every time, but at least then you don't have a server running listening for traffic all the time either.
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