The cake-frosting analogy seems spurious because a cake can taste good by itself, and so can frosting (in limited amounts). But without aesthetics you have... like, nothing (either a bunch of cubes or just a straight up black screen). Without mechanics at least you can still have a cool movie or painting or album.
Not to be contrary for the sake of it, but you can also have fun mechanics without the polish. I wouldn't call checkers, chess, etc. very aesthetically polished (unless you buy a decorative set) but their gameplay mechanics hold up nicely all on their own. Similarly, you could strip most RTS games of their graphical polish and make each unit generic shapes (with differences) and the gameplay itself would like hold up and remain fun. It really depends on the type of game, some games benefit from aesthetics far more than others. In general, though, all games benefit from good aesthetics.
Personally, in contrast to what a lot of people advise, I'm a fan of adding at least some graphical and aural polish as soon as you can (i.e. as soon as your engine is extensible enough and you aren't just hard coding everything or making it a pain in the ass to change/extend later on).
I would have to agree, I think people really underestimate the power of growing the game aesthetics with the gameplay rather than aside from the gameplay or after the gameplay. The more everything comes together in harmony the more impact the experience is going to have overall, I think.