Users don't always feel comfortable writing to your support team and that's fine. This is why you need to provide them with a way to quickly find helpful information by themselves.
Another thing is, by having a help center you can significantly reduce your customer support costs. It needs only your initial investment of time to populate it with content and then you can take some load off of your support team and automatically convert all your frequently asked questions to frequently answered ones.
Having a customer support help center is shown to lead to happier customers and having a good internal knowledge base to a happier team.