I can see the value of having multiple local working copies for various reasons, but I don't see what the point of the middle "tier" is if everything pictured is a true clone.
Having multiple working folders is useful because it allows you to segregate tasks from each other - each of the "work" repos could be a different branch, or could be for a different task even in the same branch. For instance, you might be using one to track down a defect while other work is in progress elsewhere. I do this sort of thing all the time.
The reason the middle tier seems needless is because each of the "work" repos could push/pull directly back to "server". But doing it through the middle tier requires extra push/pull steps.
Now, another interpretation depends on how strictly a clone is a clone in the diagram. Mercurial also has a "share" command (extension) which behaves similarly to clone but does not actually duplicate the entire repo history, but instead utilizes one copy of it for multiple working folders. These "shares" push/pull just as if they were cloned normally. So if the "work" repos were created by using
hg share then indeed there are benefits - they will be quicker to create, and use far less disk space.
In other words, it would be
hg clone from "server" to "local", and then
hg share from local to "work".
This is the only good reason I can think of specifically for the arrangement in the diagram.
Personally what I do is a little simpler:
I just designate one of my local working copies as the actual clone of the server, and then share that to as many other copies I need. I think this is as lightweight as you can get, without sacrificing any flexibility.