There is no reason why teachers shouldn't be required to do this, too. Indeed, if they were, the public would undoubtedly have greater respect for teachers' qualifications. It's true that this kind of test won't show who can put across the material and who cannot, but few beginning teachers are experts at presenting a lesson. Assessments requiring that and other performance skills should be postponed until the end of the probationary period when they should be a condition for attaining tenure. No matter what other qualities prospective teachers have, they won't do a decent job without a good grasp of the subject matter they propose to teach.
Some states already have pre-certification tests.
Maybe it's because they are afraid that serious tests would lead to massive teacher shortages. A few years ago, this would have been much less of a problem. So we had less trouble attracting highly qualified people to the teaching profession, and many of them are still on the job. But now, race and ethnicity and sex are no longer the same kind of bar to good jobs in business or the professions. So given the conditions teachers work under, the salaries they receive and the lack of dignity that often goes with the job, few top graduates are likely to consider teaching.