Grammatical gender lets you be very precise with fewer words. I can say in German with just 4 words both "I am on the hill" and "I am passing over the hill" by just changing the case of one word. It's the same sentence but only one letter changes and it completely changes the meaning of the sentence.
That doesn't have anything to do with grammatical gender, it's because of noun declension that that is possible. It's only incidental that nouns of each of the three genders decline differently; case distinctions could still be made even if there was only one gender.
If you are going to have to remember an attribute for every single noun it should really be a MEANINGFUL one instead of something utterly arbitrary like gender. Some examples are animate or inanimate like Algonquian languages do or the physical properties of an object, such as its shape, size, or consistency like the Athabaskan languages do.
