Contradicting highly ingrained precedence rules for the common operations (+, -, ×) is a huge flaw for strict left to right parsing.

And for ?:, only the part between the ? and the : is implicitly paranthesized. In "a && b ? c : d || e", you need operator precedence to decide if this is "a && (b ? c : d) || e" or "(a && b)? c : (d || e)" or any other combination. So you have to define the precedence of ? and : in relation to other operators in order to define the syntax of your language, so I think it's normal to consider it an operator as well (and I'd say the same for Python's if/else conditional expression, "a if b else c", this is not about the characters used).