This is a problem of dispatch. Not so much of type inference... The problem with dispatch says that if a method gets overloaded too much and too often, then programmers tend to make mistakes when they assume how the method they call will work.
You should be insane if your program accidentally confuses people with missiles, but I understand that this is a stretch to amplify the point. What tends to happen in practice is that eg. the same method which used to only read something from the local storage gets a new overload that goes out into network, and brings with it a whole new bunch of problems the calling code wasn't prepared to handle. Or, when a string was passed to the method that used to do something simple, and then the method gets overloaded with a more sophisticated method that interprets substrings in the passed string as commands to run some code -- and then you get security problems.
Have you ever seen the IntelliJ interface when it deals with Rust code? I'm not sure if it does the same for other languages with type inference feature. Anyways, the idea here is that the programmer can toggle the display of inferred types to qualify every expression. So, it's really trivial to make sure you aren't calling fire() of a missile instead of an employee. And, in practice, this doesn't lead to problems. This is so because dispatch, essentially, blurs the difference between multiple different objects, while type inference is just a kind of abbreviation. It may cause confusion, but it will be of a different type: the reader might not know what's being abbreviated, whereas with dispatch, the reader may be convinced they know what the author meant, but still be wrong.