That's the point, I think. I own my computer, which means I decide whether it lies. If I want to serve "This website only works in Chrome" when it's actually cross-platform, that's my right. I might want the client to open the page in Chrome automatically, and I would have more control over the connection if I could do so, but that control would be over the client's computer. It's not a question of getting more or less control in general, but of getting rightful control over my own property.
> both operators want not just control over their computer but also what the other computer can do
Are you saying that my demand to not have a server control what my client does is an act of control over what their computer does? Like if I told you not to use your forklift to take my stuff, I'm asserting power over your property?