The issue is that he’s looking at baseline costs of $2.50 per month per user, just for the Reddit API. This doesn’t factor in other API call costs, server costs, etc. Add on other stuff, plus the 30% cut to Apple, and you’d need to charge somewhere in the range of $50-60 per year.
This is also assuming usage doesn’t change much. If usage changes dramatically, the costs can increase substantially, as it’s nearly 25 cents per 1000 API calls. He’d need to keep tabs on it, cut off high usage users on a regular basis, and likely go with a monthly (not annual) model and adjust prices frequently.
The other option is to just charge users per API request with a markup, meaning heavy users could easily be on the hook for $20 or $30 per month or more just for using Reddit.