We aren’t at anyone’s mercy.
Nobody is forcing us to use browsers from google or Mozilla.
We are all free to implement our own UA. The specs are all open standards.
What stops us from writing browsers is the sheer volume of time and effort required - hundreds of thousands of hours of highly skilled work. That is all.
In the absence of such an effort, we would be left high and dry, with no way to experience the web.
Fortunately, that isn’t the case, because some others have done the work and allow us to use their browsers.
For that, we might feel grateful.
We might also be wary, and try to be aware of any adverse consequences of using someone else’s thing. That’s common sense, but it is still not a case of being at someone’s mercy. That situation loomed when one company sought to control the standards for the web as well as the implementation, but what we have today is different to that.