These apps will then also be a lot heavier on the phone’s battery and the users patience. So I doubt they will retain the experience the users are accustomed to.

Not really, all you need is a server that does all the scraping using cron jobs/etc and creates a reddit api backend service that pushes up new content when new content is added. In this way all that extra load would be via some server on digital ocean or even serverless functions.

You could maybe even get away with the 100 calls/minute free tier if you were doing it that way. The problem is that the user can't vote, submit, comment, or check anything personalized then, which really limits the value of the third-party app anyway.

I wonder if Reddit will let arbitrary users generate their own API keys and then each user plugs their own key into a third party app as creds to stay within the free tier limits.

Right now the new "Dev Platform" (API) is waitlisted so hard to tell.