Able to solve problems faster
And solving problems faster means we spend less on support
Product demos do wonders for presale questions and drive more sales. What happens after those potential customers become real customers? Sometimes they'll run in to a problem and need our help again. And again we rely on product demos to help them through their problems as quickly and efficiently as possible.
Before we used our product demos in support, we almost always had to ask our users for a WordPress login to their site. Everyone who does this has a story about breaking a customer's site. We've been there too, so we won't log in to anyone's site unless they can also provide us FTP access so that we can fix any problems that we may cause.
I don't need to tell you how annoying it is on both ends of the equation - sending a support request is already annoying, it becomes infinitely more annoying having to provide a WordPress and FTP login and then wait again for them to get back to you. And for us, even just getting the credentials was a pain, let alone having to tiptoe through someone's live website trying not to break anything or ruin important data.
These days we have users reproduce their problem on a demo install. Sometimes just doing this will help them solve the problem on their own without even contacting us. If they are able to reproduce the problem, right there in their first email to us we have everything we need to see the problem, try solutions, test them, and then send them back to the customer without ever logging in to their WordPress site.