It ends up being quite the opposite - many, many bugs come from unexpected side effects of mutation. You pass that array to a function and it turns out 10 layers deeper in the call stack, in code written by somebody else, some function decided to mutate the array.
Immutability gives you solid contracts. A function takes X as input and returns Y as output. This is predictable, testable, and thread safe by default.
If you have a bunch of stuff pointing at an object and all that stuff needs to change when the inner object changes, then you "raise up" the immutability to a higher level.
Universe nextStateOfTheUniverse = oldUniverse.modifyItSomehow();
Old states don't hang around if you don't keep references to them. They get garbage collected.
Okay, so this sounds like it's a method of programming that is entirely incompatible with anything I work on.
What sort of thing would it be useful for?
The kind of things I do tend to have maybe several hundred thousand floating point values that exist for maybe a couple of hundred thousandths of a second, get processed, get dealt with, and then are immediately overwritten with the next batch.
I can't think of any reason why I'd ever need to know what they were a few iterations back. That's gone, maybe as much as a ten-thousandth of a second ago, which may as well be last year.
It is useful for the vast majority of business processing. And, if John Carmack is to be believed, video game development.
Carmamack's post explains it - if you make a series of immutable "variables" instead of reassigning one, it is much easier to debug. This is a microcosm of time travel debugging; it lets you look at the state of those variables several steps back.
In don't know anything about your specific field but I am confident that getting to the point where you deeply understand this perspective will improve your programming, even if you don't always use it.