It's about not being at the whims of another entity which doesn't give a flying fuck about you, and will (often without or with very little warning) change API,

It's about not being at the whims of another entity which doesn't give a flying fuck about you, and will (often without or with very little warning) change API, have 'maintenance' (either 'planned' or 'unplanned'), or just call it a day and close up shop (of their external sign in, that is - or maybe even all together). So then you need to provide a fallback on your own anyway, and now you have two systems to maintain - so better to just use only your own.