Inviting only people who support and agree with you to a meeting seems like a great way to run a company.

It depends on what the meeting is. There are situations where you might not agree with decisions being made, but undermining your superior infront of business partners is not ok.

Those are the kinds of problems you handle privately. Not in a meeting with other people from other companies.

While I agree, I also think most such meetings can be held between those superiors just fine

There might be questions asked. And then you need the appropriate head of department to answer it. That’s why they’re there while not being expected to say anything.

I’ve had to implement systems I did not like. Systems I thought were inferior to other methods. But when the decision is made, it’s made. And when asked how we plan to implement it, I answer with the plan and the steps. I don’t undermine us by expressing disapproval in the formal meeting.

It’s called professionalism.