You're changing your claim a bit. Originally You claimed giving the ingredients like that was
more accurate. Now you're saying they're equivalent, but not how "cabbage salad" gives you any more information, because that's not the case. In many contexts gives you less.
If you're speaking English, coleslaw will give you a much better idea of what to expect, narrowing it down to two major variations. No matter what the actual result, cabbage salad leaves more possibilities. You talk about cultural variation on it, but I can't find any that don't fall under one of those two main varieties. Even when I could find a rare example that did not use cabbage, it referred to the product as the more generic "slaw", not coleslaw.
What it boils down to though you're complaining that language can be ambiguous. And it is! That tends to be more a feature than a bug though. It allows ever greater levels of abstraction that facilitate more complex ideas. If you really insist on a "cabbage salad" style of speech, you need to understand that it doesn't stop at "cabbage salad". That is so general as to be meaningless for the purpose of informing me on what I'll receive when I order it. Even if there are contexts where coleslaw would be ambiguous, it will always encompass fewer options than cabbage salad. For your style of speech to work, it would have to go much further to add information to this, something like "Shredded cabbage and carrots with mayonnaise sugar salt and pepper" Even then it wouldn't be enough, because method of preparation may vary, changing the dish.
Even if I grant you that coleslaw sometimes doesn't conform to what I've described, it's still the case that it will give more information in many more circumstances than cabbage salad. Cabbage salad will win many fewer "information" contests.
And, again, you mostly already get your way in this because the vast majority of restaurants actually to give a description of the meal. What you're complaining about is that in addition to such descriptions, there's also a single term abstraction that can be instantiated in a variety of different ways.