If your home uses no grid power and doesn't sell power back to the grid, then it doesn't. If you sell your excess power, though, you're costing the utility money: a cost which ultimately is borne by others. And even if you don't, maintaining a grid connection for extremely light intermittent use carries a certain cost. Nearly all utilities don't charge line maintenance fees; they subsume that into the kW-hr rate, on the assumption the average household uses more than enough electricity to support those costs. (though to be fair, this second factor is nearly trivial).
Interestingly enough, my local natural gas utility is smarter: it charges customers $50/month (or more for commercial customers) for no usage whatsoever, simply to maintain the pipe to your home.