I think at a certain point, "the grand scheme" is too abstract a notion to have an effect on an individual. There are trillions of beings in The Culture, spread throughout a galaxy. What would any individual having an effect on that grand a scheme even look like?

But on a smaller scale, the (still billions of) beings on, say, an Orbital can have a much greater effect on things. But again, they don't often choose to, opting to let the Minds run things. And, given that the Minds are sentient beings and citizens of The Culture as well as the humans, this is more or less the same as our current delegation of decision-making to politicians. Of course there's much to be said about doing that presently, but I think it's a given that at least the Minds are not incompetent, which can't always be said about our current politicians :P

And do keep in mind that it's not "letting" humans vote on "small things" - they have the right to vote on any matter they want, big or small, and as far as my reading goes, the Minds would respect that.