Am I missing something or is submitting from the ArXiv really that unfeasible?
I think you are not really missing anything at all, except that there is not compulsion to make the set-up as minimalist/efficient as you seem to argue it should be. That is, while you and others may not find this feature useful, it's probably harmless, no? And some programmer somewhere might've thought it would be interesting to implement this, and proposed it to whatever authority, it was approved, and so on.

But, yes, there are common situations for many people (in math, familiar to me) in which the submission to arXiv is essentially simultaneous with a submission to a journal, whether or not they make use of a literal submit-from-arXiv feature. So, yes, a paper might be considered ready without-change-from-the-version-submitted-to-arXiv. Why not? (Sure, one might realize things later, perhaps upon referee reports...) 

As to whether one "has to wait until arXiv publishes..." Well, apparently, yes, since your paper won't have been processed. Perhaps someone who knows the inside workings of the software at arXiv (which surely could change from time to time) knows a trick to interact with the system prior to that, but I've never heard of anyone finding a need to do so, given the quick turnaround. But I can't help but wondering why a day-or-two delay would matter...

So I think you're right that it's a fairly useless feature, but it wouldn't be the first.