Ryzen is reasonably priced & has one socket for the 4, 8 and 6 core CPUs.
But ok, I see what you mean: anything with more than 4 cores that is affordable.
The only reason LGA 1151 has been so successful is that most of the market consists of "gamers" who are convinced that they need higher clock speed and IPC.
AM4 should only be compared to LGA 2011v3, which has a very inflated price.
If you care more about core counts than single thread clock you can find used x58 dual socket workstation MBs which also have support for large amounts of server ECC ram which is very cheap.
Get a second hand workstation on ebay, don't get individual components.
Anyway, the machine runs an, admittedly overkill, GTX 1070 with a TDP of 150W, so the CPU power usage is the least concern.
Also, since CPU's are idle more of the time than under load the savings by using a newer CPU like Kaby Lake or Ryzen could be interesting. There is also the motherboard. Newer boards consume less power because the chips are on a smaller node.
But I guess the money you saved on buying the CPU will outweigh the electricity costs even in countries where electricity is expensive.
Unless he's running 24/7 and paying way too much, yeah, by a large margin. Even these older Xeons weren't that bad at energy saving.