It's possible to use erasure coding to avoid needing that many more copies. With 75% erasure blocks you can lose any 75% of the nodes hosting the data without compromising availability, and that only requires the equivalent of four copies. Moreover, distributing that number of copies has negligible overhead when data is requested much more often than it's modified, as is normally the case.
It's also possible to cache lookups in the same way as DNS by having larger nodes cache the lookup data and having smaller nodes query them, so that the most common queries are satisfied using a single request to a lookup cache.
Meanwhile the advantage of a P2P network is that most of the nodes are client devices which would have been powered on regardless, instead of needing additional devices dedicated only to hosting data.
Bad assumption: Most people use laptops, which aren't "powered on regardless", or mobile devices, where the power consumption of being active on a P2P network will kill the battery.
The people using laptops wouldn't leave them on longer than they would be otherwise, you'd just get the data from the one that happens to be on at the time, so they'd be "powered on regardless" for the same period of time they would be otherwise.
Moreover, the average mobile device spends something like eight hours a day (while the owner is asleep) connected to the charger where battery life is irrelevant. So give the network two modes, one where the device participates fully in the network and is a preferred source for data and one where it only registers what it has with another node and is then a provider of last resort for data not otherwise available elsewhere, and operate in one mode or the other depending on whether the device is running on battery.
Notice also that the amortized number of hits over the whole network is one per object per device, i.e. the average number of times a node has to upload each thing it downloads is only once. That doesn't take an insurmountable amount of battery even if you couldn't shift most of the load to the devices that are plugged in.
Does it need to be always on though? Scuttlebutt-like gossip networks and caches might be more what I was thinking about. In the ideal case you find the content local to you in one request, cache it, and the solar-powered server is none the wiser.
The network might be slower overall but we're talking about optimizing for lower power consumption so I feel like that would be a lesser priority.
Now I'm starting to wonder if there is a away to simulate the power draw of such a network.
It's also possible to cache lookups in the same way as DNS by having larger nodes cache the lookup data and having smaller nodes query them, so that the most common queries are satisfied using a single request to a lookup cache.
Meanwhile the advantage of a P2P network is that most of the nodes are client devices which would have been powered on regardless, instead of needing additional devices dedicated only to hosting data.