What world did you live in during the last decade and a half? One where twitter didn't famously open up to APIs then limit them then open up again?
Twitter's first API
The very first instance of the Twitter API was
before the app store and was an initial offering letting anyone develop apps that linked to twitter so long as they authorized correctly...
Limits begin to be imposed
Over time twitter started to get more restrictive, but again, there isn't any sense of developers not having 'permission' to access the API
2020 Changes
Going in the other direction, in 2020, Twitter opened back up to third parties again, once more trying to encourage third party innovation
Furthermore, while I don't know if the apps used the free or premium tiers at the end of their life, there is further evidence that Twitter was quite open to third parties since they were trying to monetize their access!
Monetization of the API
Finally,
Twitterific and Tweetbot need money to continue development over time. Given Apple's disregard for developing a saner App Store incentive structure there is little choice left to developers but yearly subscriptions that ensure they can finance continued development.