I agree and I'd say that area is almost, in some intuitive way, the more basic thing and multiplication follows from that (although I know that's not mathematically true). The definition of multiplication for natural numbers is repeated addition (e.g. 3 x 5 is defined to be 5 + 5 + 5). Many people would see that as the count of a 3 by 5 grid of objects, and that's certainly how we'd explain the commutativity of multiplication in school. If those individual objects happen to be unit squares then you have area.