In short: Very, and, Not At All
[There are a lot of generalities presented here; they reflect my limited personal experience and personal perspective in dealing with vertical organizations.]
"Organization" implies order. Order implies uniformity which in turn implies standards. Imposing a standard over distance and time has benefits, the most important benefit is the preservation of tradition, and this is very important.
Preservation requires conformity and conformity is reinforced through camps, seminars, testing and promotions (not necessarily achieved through testing).
Promotion rewards conformity. Promotion is status and status is power. Promotion elevates the status of everyone involved, most importantly the "promoter." The higher a student's rank the less likely they'll leave an organization. This relationship binds an organization and reinforces the status quo.
So what's the problem?
Isolationism. Fear of retribution for practicing outside an organization. Fear of speaking up against perceived wrongs. This relationship demands that organization officials be incorruptible paragons of altruism and virtue. This is too much to ask of any human being..
Happily the (un)spoken rules about training outside one's organization are melting away. As the next generation of sensei become figureheads, each will have their own connection to Hombu Dojo and hopefully the problems cited here will lessen (if there's anything to be learned, then there's hope).
So, organizations are important when they function to preserve tradition. They're not at all important otherwise.