It's tough to try to guess what "the Illuminati" is up to, because like you say it's just rich and well connected people doing things, it likely isn't some monolithic group with a singular focus or perfect coordination.
That said, I think an aspect of control is that you want to control the opposition too.
If you know a decentralized ledger is the next step of what things will evolve to (knowing it'll be created at some point by someone and that it's not realistic to suppress it forever), you may as well be the ones who create it.
And then at least they're able to have a large chunk of the world's treasure when the paradigm flips. (Plus maybe have some control of the timing, if they control or influence some of the lead devs.)
So I wouldn't doubt that "they" are involved in Bitcoin somehow, but not because they're using it as a means to some other end like a global currency. Just because it's a rational way to adapt if they want to maintain control/power/money for longer.
I think the powers that be are often adapting to the natural tide of things and "influencing" or "manipulating" where they can rather than writing it out with perfect control.