Wild paw paws with high levels of acetogenins announce it, with horrible flavor. The domestic fruits are selected against. A correct amount adds a lot of complexity to the flavor, so can be desirable in a fruit that you eat just a month at year. I bet that you never worry about the fact that your potatoes have a little bit of solanin after all.
In fairness, solanine is purely an acute poison, while annonacin has cumulative effects. Not that the compound itself bioaccumulates but the damage it causes does.
If you already have any parkinsons symptoms whatsoever, pawpaw amounts greater than 0.2 fruits per year have been shown to worsen them.
I'll take advantage of your post to remind that the paw paw belongs to the family Annonaceae.
Is important because there are a lot of delicious tropical fruits and fruit hybrids in the family like Cherimoya, Atemoya (Gefner, Achta), Sugar apple, Anon, Guanabana or Soursop. Annona alone has 170 species so expect a lot of tasty stuff.
If you visit a tropical country you will found delicious recipes, juices and icecreams made of those fruits. Remind that a moderate consumption is key, as all Annonaceae may have Annonacines in different amount. Soursop/Guanabana being one of the worse in that sense.