It makes you think out of the box a little bit and not linearly along the equation in front of you -
1/3 “of THIS thing” = 1/6 “of THAT other thing”.
I do think the triangle thing is just an ok example. My preferred example would use numbers.
At a third grade level I think it is good to say that 2/6 is equal to 1/3. And this can be easily shown with manipulatives. And then simplifying fractions as a numerical operation is an easy follow-on.
But young people who are just learning fractions, and who are too young to really handle abstract concepts, should NOT be taught that 1/6 is equal to 1/3. At that level, it is simply an incorrect statement. Sure, you can twist your head around and say, well, under the following circumstances, sure, I guess I can see why 1/6 might be equal to 1/3 ... But that sort of “clever” thinking isn’t a good way to introduce a fundamental concept to little kids.
I think that approach really leads into (and I think this is somewhat intentional) the thinking that “anything is true” is you just think about it the right way. Your Truth may not be My Truth, but both are true, because, hey, if you think about it the way I think about it, then I’m just right.
Certain people want that mentality to be endemic in society. And saying that 1/6 is equal to 1/3 is a step in that direction.