That’s a very good question, and not something that there is any current research on AFAIK.
An immediate thought is to point out that Solid is not blockchain, which is a favorite amongst those pointing out (justifiably) the horrendous use of electrical power by some cryptocurrency miners. Than again, not all blockchains are based on proof of work, and there is a growing focus on this problematic side of blockchains, so this might not be that big of a problem in the future.
Solid is built upon the existing web, so it doesn’t require any big shifts in infrastructure, which is also useful in keeping the footprint down.
Speaking against Solid is the fact that decentralization of data might result in more movement of data across server clusters and aggregation of data on servers that might not be as efficient if data had been more centralized. But if this is the case, I still think there’s more value in decentralization of data for us as a society, and I don’t think there’s that much to save anyway.
I think a lot of comes down to “How much energy does Solid require compared to X”. Right now there’s not that much to go on, but I hope we as a community can value choices that keep the energy consumption at a low.