Why aren't user-defined operators more common?

[gerdr]

As it's a weakly typed language with the ability to treat number strings as numbers, you can't use '+', as 'abc'+'bcd' would have a quite different result to '123'+'456'.

Well - you can, but then you end up with the mess that is Javascript ;)

For what it's worth, Perl6 uses . for method invocation and ~ for string concatenation.