That would be interesting in itself, but I doubt it would go far.
The vessels would need to "refuel" on the way, and most trading stations are in direct control of the European powers. Then, once they're there, the markets would be closed as a lot of that control is, as you pointed out, under state monopoly. Even the big merchants would have stakes in the companies.
On top of that, there's the question of motivation: the bulk of the revenues does not come from the Indies-Europe trade but from the Indies to Indies trade