Hmmm, your last link shows that Moose uses inline tests; if it is a popularity contest, that is one heavy vote in favor!
I doubt that :) Moose only has 10 authors. Its only used for the cookbook.
OTOH, Test::Inline isn't always listed as a dependency, http://grep.cpan.me/?q=%3Dbegin+testing reveals a few more distributions that depend on it ... kinda not really (at least a few authors tried it once upon a time)
Extracting tests from pod seems a bit backwards ... embedding makes a bit more sense, but still seems like busy work ... but installing the tests and telling the user to UTSL for complete/runnable examples? That seems "just right" :)