My husband and I have two anniversaries. One is the day we became a couple and the other is our wedding date. For the former, we went to a Turkish restaurant and it was only afterwards, when my husband asked to have the remainder of his meal wrapped up, that I remembered that you can do that here. In Japan, the custom is rather different because cleaning your plate reflects satisfaction with the meal. Also, leftovers are less popular there than in America. People like to have fresh food and the notion of enjoying the rest of your restaurant meal the following day is unappealing. Additionally, the portion sizes are generally smaller (though not always), so there rarely is enough food left to make packing it up worthwhile. Even if there were lots of leftovers, most restaurants in Japan would be a bit put off, if not utterly confused, by a request to put the rest in a doggie bag.
I won't miss the fact that taking the remainder of an (often expensive) meal home is pretty much off the table in Japan.