The problem is that going to Aphrodite is a superset of not going to Aphrodite. You get everything an MC who declines the opportunity does AND more. As you say that can work from a purely roleplaying perspective, but only if we do the heavy lifting ourselves. Nothing in-game changes if you're a 'good boy.' The MC isn't less jaded, he isn't more naive, he doesn't feel less guilty, he isn't curious about what he missed, he isn't even richer for saving the money.
The choice is - at least thus far - no different than offering us a button to skip the scene. And based on OiaL, I doubt that will ever change. We can pretend the decision ties into the nature of our MC if we want, but we could do that just as easily with a skip button, too. These sorts of options aren't dilemmas to ponder, they're formalities that let us opt out of a scene if we really want to.
That doesn't make this a bad story by any stretch, but it does diminish the game aspect, at least IMHO.