To present an undergraduate analogue: in elite colleges, which invariably and intentionally lack business programs, economics programs have a large number of douchebags in them who see "econ" (they never call it "economics") as a pathway to investment banking. Real economics students hate sharing classes with them.
In colleges with business programs, the douches tend to gravitate toward the business degrees, and leave the economics students alone. Just as with economics, which has many serious students, there are non-douchebags who also pursue business degrees and MBAs, obviously, and I'm sure they hate sharing classes with the power-seeking douchebags as well. A lot of really good people go through MBA programs into management. But douchebags also also follow that track, because they follow money and status; it's how douchebags operate.
However, it's not even accurate to say that douchebags are the problem, since there are about as many of them (give or take) as in any other point in history. The difference is that the post-1980s mainstream corporate environment favors and promotes those prone to overtalk, power-play, and "hunger" (corporate euphemism for greed)-- in other words, douchebags. Douchebags thrive in environments of superficiality, conformity, hierarchy, and opacity of contribution. So now you have a system where, despite the best efforts of business-inclined and talented non-douchebags to pursue MBA programs and management tracks, they cannot ascend in the majority of corporate hierarchies, because most companies have filled their upper ranks with douchebags.
MBA programs don't cause this problem. The money and status they offer attracts douchebags, but I've seen absolutely no evidence that they encourage more people to become such. Moreover, the problem isn't that there are more douchebags alive than there were, say, 30 years ago. The fundamental problem is that large, hierarchical corporations now select in favor of douchebags rather than against them. What degrees the douchebags have has nothing to do with this.