If you wrote the code to have a single exit, the cognitive load was also typically lower, as the control flow could be thought of as one way in, and two ways out (return or exception). Good disciple also followed "the jolly good idea of Demeter" or whatever it came to be called; that being to only operate on the state (or preferably, values) passed in, where possible.
In my experience, having multiple exits is even better because I can check which edge case is being hit by placing multiple breakpoints, or a breakpoint at a specific exit I want to check. I understand the pain of having to step through the code to get back to a certain execution point, but I’ve never been in a situation where multiple exits caused such cognitive load as to hinder that process further.
When I began writing C# I recall my other team members "refactoring" my code to be shot through with multiple exits instead of a my collecting variable, because "it looked nicer." When they asked me why I wrote it the way I did, I mentioned the Java debugger thing, and they kind of looked at me blankly and said, "Huh, never thought of that."
Times change.