Yes, you have associativity right. The question is what kind of price you pay. Allowing a user to type ‘a+b+c’ seems reasonable and forcing them to write ‘a+(b+c)’ seems draconian. But what does ‘a/b/c’ mean? Does your grammar have to have different productions for associative and non-associative binary operators? For general operator support do you have to have productions for every operator, or do you add a little bit of state to your parser outside the grammar to handle the lookback to determine if the same operator is being used? These are ugly decisions to make for the smallish benefit of being able to omit a couple of parentheses. And how often does it really occur outside of heavy numeric computations, which are kind of the minority.

Some APLs go overboard here and just say that everything operates right to left so 2*3+4 is 14. This is super awkward but once you get used to it it’s kind of a relief to not have to think about operator precedence. Similarly RPN and Lisp dodge the issue.

In my experience operator precedence causes actual bugs, but associativity rarely does. So despite all this I’m not firmly against associativity, but I’m getting there.