"I hate to break it to you..."
Everything you wrote it is incorrect. I gave you specific examples. I am quite aware of my power, both under the rules (without requiring any court intervention) and, in general, as an officer of the court. If you are not aware of this, I don't know what to tell you.
Next, you seem to fundamentally misunderstand how to analyze this as a barrier to entry. So let's look-
First, does it work to prevent too many attorneys from practicing? Empirically, the answer is no. If anything, the bar (heh) is set too low.
Next, let's look at your argument re: ABA schools getting a free pass. Initially, this argument can be dismissed for the same reason you dismiss the bar exam, but at an even deeper level. Many ABA schools teach you nothing substantive about the practice of law in a particular jurisdiction. They are filled with electives, and don't have a set curriculum after the first year. Even if your school offers jurisdiction-specific classes, that will not account for people that want to practice, initially, in a different jurisdiction. Finally, and worst of all, there are two types of schools- those that work hard to keep their students in (in other words, you really have to affirmatively screw up to fail out), and those that fail out large numbers *because they admit to many that cannot pass the bar and they need to keep their ABA accreditation.* IOW, for both types of schools, the bar exam operates as a necessary filter.
In short, your analysis is just that the bar exam isn't perfect. No, of course it isn't. Neither is the LSAT. Neither are the exams given to LEOs for admission (!!), training, certification, and promotion. But I'm glad we have them. Given the state of the profession, I think the least of the concerns is that barrier to entry is too high.