If you are a member of the co-op, sure. Not everyone who trades with a co-op is a member. If you are a shareholder, in a company, most likely you have votes, as I think less than 10% of companies have different share classes with unequal voting rights, and of those most still have some voting rights. So in both cases (with limited exception), shareholders have voting rights. So there is no difference here, in fact all of the things you listed is valid for more traditional businesses.

The main difference, at least for the cooperative I worked for, was that no individual can have more than 1 share, where as in other incorporation models individuals can have more than 1 share. This is advantageous as one individual can expend resources to buy shares, then use the control granted by those shares to improve efficiency and the value of the shares they acquired, and everyone who is a shareholder benefits from this. No similar mechanism exists in a co-operative.

Maybe, with a cooperative, on a small scale, you can lobby enough people to effect change, but it takes a lot of time, and usually the people with time to fiddle with the politics of a co-operative probably should have as little as possible say in how it is run as they likely have nothing more productive to do.

I do vote in some co-operatives, I even vote in the co-operative I worked for, I look at the candidates, and I can clearly tell that there is no way they will change anything, never mind do something as drastic as replace the inept leadership. I could of course expend lots of time to try and convince them, but this is a massive gamble.

If I see a company is ran poorly, and I have money to buy enough shares to change it, the gamble is a lot smaller. I know it takes X resources to aquire Y% of control.