Wait — have you talked to many architects? They have plenty of complaints about their lack of control over projects. The rockstars (Koolhaas, Ghery, etc.) are a tiny minority who are often hired because of their unique vision. But (from my anecdotal understanding) the typical architect of an office building or cabin has a far more pedestrian, and frustrating, experience regarding the vision of their projects and control over budget/priorities and more.
You might be right that on average they have more power than the average product designer, but it’s worth verifying the claim. The grass might be always greener.