It would if you had to continue the airstream indefinitely until your mouth was closed¹, but we can also stop the airstream of a vowel without closing our mouth

It would if you had to continue the airstream indefinitely until your mouth was closed¹, but we can also stop the airstream of a vowel without closing our mouths at all (I guess either by using a stop further back in the vocal system, or disengaging the muscles that are producing the airflow²). So in practice, there are other ways to end the production of a vowel without producing a /p/. ¹ I haven't thought clearly about how nasals affect this, but it seems like still another possibility is to allow air to exit through the nose, producing /m/ instead of /p/. ² When I try to pay attention to what I'm doing when I deliberately stop a sustained vowel, it seems like I'm using glottal or velar stops much more often than I would have thought. Interesting!