Most applications are not supposed to survive a panic!(), to the point where I personally tend to use "panic = 'abort'" for any code where performance matters. As such it's not really a mental overhead, and definitely not the Rust way of doing error handling (in the same way than using "assert" and a signal handler is not the way you're supposed to do error handling in C++).
The Rust way of dealing with errors is to return a Result<> and in my experience it's the best system I've used. It doesn't have the code flow breaking aspect of exceptions while being a lot nicer and less error-prone than C or Go style error handling.