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Clearly, you can NAT an entire nation! IT JUST WORKS!
(Of course, the fact that one of the most reclusive and oppressive nations in the world is using this isn't a shining endorsement, but still....)
Sure, but your big NK router only has 64K ports per external IP address. It will probably croak well before it has 64K NAT sessions going, though.
The worst downside (besides having to set up and manage the thing) is spam control. Gmail is excellent at this, and Postfix/Amavis/Spamassassin only catches a fraction of the incoming bad stuff. There are cloud services for spam filtering, but they seem expensive for a single user.