I completely agree, it's just a way for us to fund development of our free games, (I know there's pay what you want) but our games already have in app purchases for mobile, so instead of ripping all that out might as well just incorporate it.
What makes us want to go this route, is the in app purchases have nothing to do with game play, and add a few minor things like 1 extra boss and character and cosmetics.
Viewing post in In app purchases?
If you can incorporate this into your existing infrastructure, all good for you. If that fails, you can fallback to link to your Google Play store for the mobile version. You can even go old school and sell access to a password for benefits.
I suggest you search for games that actually use this oauth feature, to see how they are using it and how they handle dlc.
Logging in to play is just not seen all that often on Itch.