US browsers account for more than 90% of the market share though. The main non-US browsers are Opera (Norwegian company majority owned by a Chinese company) and Samsung browser (South Korean company). Both Opera and Samsung are based on an American controlled open source project (Chromium, controlled by Google).
So for the vast majority of people in the world government ownership of their browser would mean American political control. The current administration has expressed both in theory and practice a willingness to directly exert influence over organizations even when they are supposed to be independent of government control. That would be a concern for much of the world even outside the US.