inefficient in the sense that

• traffic go over the internet rather than internal networks which means the routing is much longer, over slower links
• not to mention that in distributed systems information frequently is duplicated many times rather than referenced on some internal system (sending out an email to 20 people duplicates that email 20 times across many providers rather than simply referencing an internal ID… you can just centralise content and send out a small notification message, but that’s generally not what people are talking about when they’re talking about modern distributed systems)
• each system can’t trust any other, so there’s a lot more processing that each node has to do in order to maintain a consistent internal state: validating and transforming raw data for itself - not usually a particularly big task, but multiplied by millions per second it adds up fast
• hardware scaling is simply not as easy either… with centralised systems you have, say, 1000 servers at 95% capacity (whatever that means): you can run them close to capacity because your traffic is generally insulated from load spikes due to volume, and generally you wouldn’t get 5% more load faster than you can scale up another server. in distributed systems (or rather smaller systems, because that’s implicit here unless you’re just running the hardware and software to duplicate the whole network, which would take more servers anyway due to the other inefficiencies and now you’re multiplying them) you need to have much more “room to breathe” to absorb load spikes
• things like spares and redundancy for outage mitigations also become more expensive: if you have 1000 servers, having a couple of hot spares (either parts or entire systems depending on system architecture and uptime requirements) isn’t that big of a deal but in a distributed system you probably need those hot spares, but all of a sudden every instance needs those hot spares somewhere (though this can be seen as a similar issue to traffic issue: spares of all kinds are just unused capacity, so the higher your ratio the more under-utilised your hardware)
• this is all without getting into the human effort of building systems… instance owners all need to manage their infrastructure which means that the mechanisms to handle things like upgrade without downtime, scaling, spam protection, bots, etc have all been built many many times

NONE of this is to say that they’re worse. in many ways the have a lot of advantages, but it’s not a clear-cut win in a lot of cases either… as with most things in life “it depends”. distributed systems are resistant to whole-network outages (at the expense of many more partial network outages), they’re resistant to censorship, they implicitly have a machine to machine interface, so the network as a whole is implicitly automatable (that might be a bad thing for things like spam, privacy, bots, etc), but people tend to generally be pro-bots and pro-3rd party apps

Idk what to say to this. Is it true? I don't know, and you probably don't either. That's a weird way to look at it and I doubt anyone has measured the power costs of the global email network.

It's also useless for decision-making. What matters is a question like "how much would it cost me to host a server and contribute to the network?". Even if the total global cost is billions of dollars, the network will continue to grow because nobody has to pay all of it.