now humbly eating crow, as I seem to have my sources confused. While Kokan Nagayama sensei does mention a "distinctive carved groove" in defining a naginata, he does not use it to differentiate between the two, and his diagrams clearly labeled "nagamaki" depict a naginata hi.
Thanks Franco. I knew the quoted writings and also have its original Japanese book. The correct quotations are as follows.
Kokan Nagayama sensei did not say that naginata-hi always difiines naginata. He only said that it it was a feature often seen on naginata.
So as you already mentioned, I assume that there are some naginata without naginata-hi and there are some nagamaki with naginata-hi.