I worked for an ISP that offered such a plan. You were never charged any overage fees, and there were no hard caps on your monthly hours, but we reserved the right to limit access on a per-case basis for heavy users, and to prioritize usage (back when we had user-to-line ratios) to limit heavy users during peak hours to ensure all customers could use the service. We were very clear about this in our signup sheet too (it wasn't buried in the T&C).
It works well for the 90% of the people who have "regular" usage patterns ("regular" being defined by the provider) and just don't want to have to keep an eye on their usage.
It doesn't work for the 10% of heavy usage customers, or the folks who think the provider should be held to their own personal definition of "unlimited" (i.e. "unlimited means I should be able to stay connected 24/7 all month long!!").
All that said, I think Republic Wireless should be a little clearer about what unlimited means. They're trying, but I think it's still a bit vague at the moment.