‘Meaning’ is largely a social phenomenon, and ultimately ideological. If all you see when you watch anime is “Due to a number of outrageous coincidences, a guy lives with seven other women encounter a number of problems only he can fix” than you have totally missed the point. Granted, there are some shows which have very little else to offer that their basic plot, and they can be very entertaining. But most shows at least have a “point” and meaning other that what is specifically stated.
I offer Kino no Tabi as one of the “deepest” shows I have every watched. This show forces you to consider what messages it is presenting, and apply you on ideology to the story. Of course I cannot give it universal justification, but that is the very beauty of story telling, meaning IS subjective and relative to the spectator. Of course he or she must actually apply themselves to find it.
Take a look at any movie, anime, TV show, or example of the like; you will see that not all of them tell great stories, or have much to offer in the way of meaning, but the best ones do.