A couple of interesting points you bring up, although probably not by intention:
A: An MBA is a credential, not necessarily a skill or set of skills. Earning an MBA is applying yourself to learn a set of skills, and then convincing the instructing organization you have learned the skills. Why get an MBA if you can circumvent it and just learn the skills? Why even bother with the superfluous skills and instead only learn the necessary skills on the job (and get paid for it)? With your MBA you can convince someone that you have some set of business skills, and that you are capable of applying yourself.
B: There is a different culture of employment relationships between America and say, Japan. In Japan, you are typically employed by the same company for life. Job hopping is rare, and there is a lot of loyalty in the employee-employer relationship. Why would you get an MBA in such a culture? You can surely learn the necessary skills on the job, and you most likely will not be leaving the company to find a better opportunity. Branching off from point A that an MBA is a credential, it follows that such a credential is not needed as much if you aren't planning on using it to unlock external opportunities. The flip side to this is that in America, an individual might find themselves working 2 or even 3 'careers' in their lifetime, and job hopping isn't considered disloyal, it's being aggressive. A credential is much more important to someone in this culture, as they will need it to convince new employers to hire them.
A counterpoint I want to bring up in support of an MBA is that an MBA readies you for the job you may have 5 years from now. You indicated that the necessary skills could be learned on the job. But training a new manager is expensive and risky. First, the manager must take the time to learn the tools, making him or her less effective. Second, there is the risk that this person is simply not management material, and that the investment will be wasted. Having an MBA shows (in theory) that the candidate is management material, and in fact has already learned many of the necessary skills. A company looking for a manager gets to know that this candidate is more likely to work out for them.
Finally, you said "If a person cannot learn that on those skills on the job, I seriously would question his/her ability to be an effective manager." The actual purpose of the MBA degree is to show that the candidate does have the capacity to be an effective manager. Again, it's a credential that is designed to remove the risk of a poor hiring decision.