Scala has neither operators nor operator overloading and I don't know any library which "encourages" doing those crazy things.
There are a few places where symbolic method names are used, and in pretty much every case, it is well-established prior art: +, -, *, /, etc for math operations, ! for sending actor messages (Erlang), &, | ,^ for bit operations (C and friends).
Regarding the type system ... well, the alternative is stuff like reflection and casting. Both introduce the possibility of runtime failures and make refactoring and reasoning a lot harder.
Sure, sometimes a well-placed I-assume-this-can-never-fail cast is exactly what one needs, but I'm happy that Scala gives developers another, safer option here.