If the issue is displaying ads or gathering analytics you can deal with both of those without cutting off third party apps. If you are concerned that others are building big data tools or bots off your free API you can also just grandfather the existing popular clients as free or with a very large discount.
For that matter you can also just set different price tiers for API clients that are used interactively by real people to interact with subreddits vs anyone else.
The social media game is all about network effects. Putting up barriers to making reddit a core service is only a bad thing. What positive gain is reddit expecting from killing third party clients here? As I said ads and analytics can be handled by the license agreement. You can even require them to link a library you provide that does the ad displays and analytics by pulling code from your servers so if you really must have deep control of that experience you can.