You brought up some great points there but couldn't those be generally classified as training? When I think of support I think of people who help the customer to analyze problems and fix them. If support people are spending time holding the customer's hand then I'd say it isn't fair to be tasked with support and training.
Just because it generates reports promptly without crashing every time doesn't mean it will know which reports to generate or which data to pull from, or how to include your new office statistics.
Just because your phone synchronises email when abroad without messing up doesn't mean it knows which email addresses to forward to which people.
Support people would then be primarily involved in using technology to help businesses do things, instead of primarily using technology workaround other technology's problems.