I think players don't like being under someone else's thumb. Some might see a large organization as a much bigger, much less personal GMPC. Especially if they're the only way to get cool equipment or gain levels.
This happens with superhero genres where a superhero team is supported by the government or some other organization and the players almost seem to resent it at times. They use it for the benefits, but they don't necessarily enjoy the responsibility that goes along with it.
For this reason, I only use organizations in the game that the players can join if the players are looking for that type of thing. And even then, I tend to run the organizations light handed. I tend to prefer organizations that are allies with the PCs, as opposed to organizations that the PCs are part of. That way, the PCs can occasionally call on their allies for assistance, or the organization can call on the PCs without there necessarily being that strong obligation.