DNS servers are a very simple computer that must be online and connected to the Internet 24/7. You can make it do other things too, but the important thing is that it's able to direct people who ask about your domain to your computer, even if they ask at obscure times like the very early hours of the morning. DNS is simple work, so most people make these computers do other work for them as well, like email gateways, load balancing, or some other task.
Computers use electricity to stay on. But not in the same amounts. A computer with an overclocked, top of the line processor, a massive RAID array, and deep deep banks of ram is going to use significantly more power than a budget CPU at factory set speed with a "green" hard drive. Electricity costs money. Not much, but it adds up over time.
I'm imagining a very simple embedded computer. It uses a very low power CPU. It has a modest amount of RAM. It has a flash drive with a basic OS and DNS support and configuration. And it has a robust network card. With a 5V DC connector, I store it in my local ISP's closet, where it can easily get power and bandwidth. It doesn't need hard drives. It doesn't need a monitor. It has no moving parts, and will gleefully point people to your servers for years and years and years.
The cost to run this thing is minuscule. we could get the cost of them down to maybe $80 at most if we print a lot of them, and that's assuming a proprietary CPU architecture like ARM. ISPs could store entire closets full of them for all their customer's hosting needs. Just one problem.
I can either make it reconfigurable on the fly, or I can lock it down so that it's hard to alter. If I make it hard to alter, then you'd have to go to your ISP's closet to change it, which is a pain if you have to make a lot of changes. (Changes like new domains, moved your computer to a new IP, or whatever.) If I make it able to take your connection from your desk PC, then it's so much more convenient, but runs the risk that someone may be able to hack your password, spoof being you, and poison your information with fakes. Suddenly, your website redirects to l33t Bob's house of hackery, cleverly disguised as your company's website and stealing your customer's information for nefarious purposes!
I could compromise and allow it to only connect from one IP, and require a special encryption key to do so.