This would not only be reasonable, it's a model used by other services offering APIs. Spotify which gates API access with a premium subscription comes to mind.
That's not interesting to Reddit however, because Reddit wants full control of user experience so they (theoretically) have more opportunities to monetize both users (including premium users) and their data, which probably looks better for a prospective IPO.
I wonder if this could also actually work against reddit's interests. I'm guessing that a lot of the power users / mods have the highest API load, by doing things like taking large mod actions. You'd effectively be charging them more for the privilege of working.
I'd say it's better than shutting mods and power users out of better apps entirely. They could also do things like give mods of subreddits past a certain subscriber/activity threshold free premium to help them mod better.
That's not interesting to Reddit however, because Reddit wants full control of user experience so they (theoretically) have more opportunities to monetize both users (including premium users) and their data, which probably looks better for a prospective IPO.