quoting Travis B.:

so the lack of /p/ does not require a chain shift...

...if all these onset-less words were due to consonant loss

On both of these points you're viewing what's been written a little too extreme and black-and-white, I think.  I suggest chain-shift as a possibility, and no one has claimed that all cases of word-initial vowels are down to consonant loss, just that that it could be a contribution to the skew.