Most mods (who oversee the generation of new content) use the API because third-party apps offer superior mod tools. Instead of thinking about "shutting down third party apps" think about it as "asking your volunteer labor to do the job on hard mode". You can see why those people might get pissed off.
I understand why they’re pissed off, it’s just not clear to me that they are irreplaceable. Lots of people here are talking about their favorite niche subreddit but is that really where the value is derived, advertising wise? I doubt it. I’m fairly certain that the top 25 or so subreddits drive most of the revenue, and they have no dearth of people willing to mod them. Hell, if Reddit Inc just in-housed moderation of the the top 100 subs they’d probably be fine.