That's not what I'm arguing. It's okay for that complexity to exist, I just don't think that exposing it to the end programmer is by definition a good thing. If you have a fixed set of infix operators then you can have a well defined grammar. If you have an extensible set of infix operators, then you need to make major changes to your grammar to prevent ambiguity.
The way infix operators work is a decision the language designer has to make early on. Bolting on a way to create new infix operators in Java (not that you're suggesting that) would be a disaster. I agree with you that sacrificing the "just work" aspect in the name of strong typing (OCaml) or in the name of uniformity (Lisp) is a bad trade-off.