It's not so much a matter of reduced typing as that if you're invoking an operation many times, developing a concise notation for it can cut down on the noise it creates for a reader. It should be used very sparingly and heavily documented, though, for exactly the reason you outline.

It really comes down to who you're writing the code for. For something like numpy, whose users will mostly be familiar with matrix notations, operator overloading enables a huge improvement.