Most utilities cannot just shut you off. Many states have laws that determine when and how. The biggest thing about a utility though is that you pay for usage. If you want to leave your lights on all day, they really don't care as long as you continue to pay your bill.
Personally, I don't see a problem with metered broadband, and only have a problem with the current pricing structures. Look at the mobile space to see how messed up it can be. Companies set prices at a usage level that is just below what a person really needs so they force people into the next tier with the hopes the person will not actually use it. Instead, I would support a flat rate per GB. I've seen numbers like $6/GB thrown around for mobile (it would obviously be a lot lower for line connected broadband, but you get the idea).
If we do end up with broadband treated as a utility in the US, I would bet that it will be metered and charged for usage. It's the most fair way to support the system and will naturally prevent people from doing something similar to leaving their lights on all day.