More concretely, as a (former) subscriber to Reddit Premium, I should continue to get access to Reddit via their APIs for free. But that was never an option, since Reddit only wants to charge the application creators and not the actual consumers.
Your argument is the same as saying that if I buy a can of Coke I should be allowed to use the CEO's company car for life.
It's easy for them to allow premium users API access, they'll still be developed for third-party apps with an accessibility focus amongst other things.
Reddit doesn't owe us anything. But given how easy this would be, it's unsurprising that taking the current obtuse approach makes some people not want to use the site.
This also provides providers a way to fairly monetize their API: we're giving you some basic level of access that matches what you get through the website for free, but if your access pattern is such that you put a load on our system that we can't tolerate, then we'll charge you (by providing a paid tier).