Measuring what is easy to measure instead of what actually matters is a classic fallacy.

It's a good first step, a pre-filter to more demanding questions.

There's no such thing as "filtering" in academics. You don't get to kick out the students who didn't do well on the multiple choice and only proceed with the ones who scored highly.

I had classes in school that had multiple-choice quizzes every couple of weeks. It helped students figure out if they knew the material just covered and it helped the prof know how well he did teaching. They acted as checkpoints.

The mid-term and final exams were not multiple choice (at least not entirely).

WTF. OK, clearly you're contributing to the problem too. Yes, there is such a thing as passing and failing, regardless what your ideology has brainwashed you to believe.

You don't pass and fail in the middle of the course, so there is no "filter".

You can't give someone a multiple choice test and then give a written test to only those who passed it, except at the granularity of an entire course.