> Browsers are far more battle-tested than just about any other web-facing application on your computer.
They also have a monstrous attack surface because they are "web-facing". A specialized client that only implements one protocol without any connection to the "web" is far easier to reason about and debug.
If you only consider the number of man-years an application has been battle-tested, you imply that design complexity and attack surface doesn't matter. If we account for complexity by using a metric like "(man-years of battle-testing)/(magnitude of attack surface)", a well-tested specialized client that hasn't had many recent bug reports is a much safer choice than anything running in a browser.
> blindly trust a client
That's even worse for the browser: you have to trust several orders of magnitude more code implementing a massive set of interdependent features. Yes, there are probably a lot more people working on fixing bugs in the browser, but there are also a lot of people adding/modifying features and thus creating new bugs.