I think Guttman is referring to the GCM nonce when he talks about the "counter"; GCM has a famously short nonce, so the common advice is to use an incrementing counter as your nonce rather than risk colliding random nonces. In that context, "forgetting to increment the counter" is a huge footgun, not a "core and simple feature of the mode".

(You can't really forget to increment the underlying CTR counter; your system won't work.)