For most consumer-facing sites, I think paid support is a non-option, and might even drive people away. The users tend to treat these services like they would a utility company, albeit, a free one. They just expect it to always work, all the time, and if anything goes wrong it's your responsibility to drop everything you're doing and fix it immediately.
Maybe I misunderstood your initial statement. I thought you were suggested a "paid support" model, where the users pay to get technical or customer support, much like some hosting companies charge.
By "paid support" did you just mean premium accounts? If so, I 100% agree that premium accounts are a great idea.
We consider support to be an integral part of the experience and treat all users the same in this regard. When someone emails us for support, we don't even know if they're subscribers or not. Replying to support emails doesn't usually take more than a minute anyway, so it's the least of our costs and it makes users very happy.