There are four derefences in

@{$people->{login}->{desk}->{paperclips}}
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but only three arrows.

The rest of your post doesn't relate to what I said, so I have no comment on it save that I rarely have paths that long.

for my $employee (@$employees) {
   for my $desk (@{ $employee->{desks} }) {
      $paperclips += $desk->{paperclips};
   }
}
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Four dereferences, but only two arrows. And the output of your script doesn't illustrate the structure at all. Data::Dumper will do that to some extent.

I had to do this statically, because I didn't have full environment to run it in(so no Data::Dumper). I was trying to find the structure of a couple of large state hashes that get passed around, using only what I saw in the code. I'm sorry I wasn't clear about that.

Both you and I might have written the code differently, but I had to tackle what was in front of me. This code has a lot of nested hash derefs, and when they are all listed by the command line, they form a convenient hierachy which shows the keys and sub-keys. A possible advantage over data dumper (in this case) is that it shows which keys are accessed by the program, rather than all the ones that exist.

Both you and I might have written the code differently,

Again, I didn't comment on that. My only beef was with your statement that everyone uses "->".

because I didn't have full environment to run it in(so no Data::Dumper)

I suggest you fix your broken install.