They don't want to deal with the legal implications of it. Spez has said ad nauseum that they don't want to risk 3PA providing NSFW content to users that Reddit is not allowed to serve because they don't want to be held responsible for that. Especially now that some US states are requiring actual ID verification for 18+ content.
While Spez is a lying weasel, I don't doubt that Reddit is worried about NSFW-related lawsuits, bad press, and ad revenue impact.
And, the next step after having control of the content is to further restrict it.
Reddit could require some kind of verification on the account level and still allow 3rd party apps to work though. Seems like an excuse or they are just being lazy.