I don't think that is the right conclusion to draw.
I think the key driver is what is going on is ease of use - and I am thinking more at the pedagogical end of things, rather than which button you have to press. When you create a multiple choice question, you can be sure exactly now Moodle will grade every possible student response. With short-answer, you have to start worrying about students misspelling words, and how you will grade that.
Of course, if that was the only consideration, then everyone would use true/false, and we don't see that. So, really it is about pedagogic bang for buck. MC clearly hits a sweet spot of letting teachers ask all sorts of questions, while still being conceptually very simple.
Another thing driving MC use (I guess, and particularly in the US) is the number of standardised tests that use MC - and teachers have to prepare students for those tests.
I am surprised how many essay questions there are. I suppose that once you have decided to bit the bullet and grade manually, then again essay is conceptually very simple and flexible.
In terms of whether all this is formative or summative. What I see at the OU is much more diagnostic use of quizzes - or very low stakes assessed use, awarding just enough marks to encourage students to do the activity, rather than have a major effect on their total course grade.
The point here is that if you are setting up a test for high-stakes assessment, you have to be very careful and check everything several times. On the other hand, if you are just making a self-assessment test for your class, you just need to make something good enough to be useful. On the other hand, if you are doing serious assessment for learning, you need to start writing lots of good feedback, which is more work again. Perhaps I should admin I really don't know what people are actually using the quiz for. I would be interesting to find out.