For every plea whistle, the blog says, "Pea froze, but whistle still worked." I don't know what that means because "frozen pea" implies the whistle is not making a sound. As far as I am concerned, a whistle that works does not have a frozen pea.
A conventional pea whistle is, acoustically speaking, a vessel flute. The same as an ocarina, and obeys the same equations as an vessel flute. Even with the pea jammed in place, or removed altogether, it will generate a steady tone. I had a couple of de-pea'd (neutered?)whistles, and aside from having a lowered pitch, work as well as the unaltered models.
Just a though, but if any of the manufacturer's are listening, an open ended whistle, instead of the conventional close ended whistle, would make debris a lot less of a problem. Getting pocket lint out of the bottom of a small whistle is a pain in the rear. Blowing it out the end of a open ended tube, not so much.