I think human nature is such that any cooperative can work up to a limited size, kind of like primitive tribes - up to 150 people. In order to do your part honestly, you have to know most/all members personally, otherwise an incentive to slack on the job is too tempting...
And then one sees the manager/coordinator, sitting on their ass in air conditioned office, while most others are sweating outside (in case of farms) or in the workshop/garage...
You're right that cooperatives above a certain size can't be direct democracies. I do think we need to be able to cooperate at scale in a democratic way, like representative democracy - otherwise how do countries work? (Not very well some might argue) but if we don't develop an alternative to the googles and amazons of the world then we'll never outcompete the current system.
Please don't use terms like 'primitive tribes' - whoever you think of when using this word might want to discuss the definition of 'primitive' with you. Because whoever limits their group size to about 150 ends up being less primitive than those who never question the infinite growth of everything.
I'd argue that this is a benefit. Too many companies are way bigger than they need to be. Instead you could take a more federated approach and have a cooperative of cooperatives. Each location would be it's own worker owned business, and each of these would in turn get to work cooperatively together to decide on branding and larger strategy. You could have representatives from each store and maybe still have everyone vote for a cooperative president.
I don’t disagree with your premise but I do think the latter two should be mostly avoidable as issues. If the workers are involved in the decisions then they would be able to spend (or decide it is not worth the expense) on cooling technology (AC for indoors or any other outdoor/personal solutions). Seems less of an issue than saying corporate doesn’t care etc.