LIZ sounds like the voice of reason to me (not to dismiss some of the other good commentary so far), and I enjoyed her "true confession" about the pork bun. I agree that this thread seems to be going around in circles while touching on some odd side tracks. (Children's concept of time? This may be a more serious matter if they need to go potty, but isn't learning to defer gratification an important part of their upbringing? I actually would be more worried about seeing an excited or exhausted child wandering around a depachika with food in their hands than I would about a grown-up. And if you want to invite disapproving stares from the natives, letting your kid to that is sure to do so!)
It is frustrating for a lot of foreign tourists that indeed, there is often no convenient place to consume the items purchased in a depachika. In particular, eating them while walking around the store, as if you were on the street and the items were intended to be eaten as street food, is just a bad idea. Yes, these places are often way too crowded for that. Even if the depachika is not crowded, it is just too easy to get distracted (there are a lot of distractions in these places!!) and let your guard down. Accidents happen, and if you get yakitori sauce in someone's hair or your child gets bean paste on somebody's 30,000-yen silk blouse, it is not going to be a happy situation.
One place I like to go for a depachika experience is the Shinjuku Takashimaya. There are places to sit right outside the door (in a covered area protected from rain as long as it isn't crazy windy), and some people also eat out on the terrace facing the tracks. I have seen many Japanese people eating lunch there and I feel comfortable doing so myself. Of course, it can be too cold in the winter. I find the Shinjuku Isetan to be more eye-popping, but there doesn't seem to be anyplace to eat there. There is certainly nothing wrong with Takashimaya, especially for a first-timer. Of course, that assumes you will be in Shinjuku. The Ikebukuro complex referenced above is another favorite of mine (but I never found a place to eat there). As for rooftops, I used to go to places with department stores that had them, but they seem to be less and less common these days. You definitely cannot count on every store having a rooftop area where you can eat. Some still do, many don't.
I have loved depachikas since the very first time I went to Japan, although after many years they have lost some of their appeal for me. But I still cannot resist them! On every trip to Japan I make "self-catered" dinners made up of take-out items (from depachika and other places) a part of my meal line-up. I sometimes spend an hour or more buying the perfect items (including beverages) and then consuming them in my hotel room. These feasts are something I look forward to and really enjoy. However, I will say that they are definitely not the cheapest dinners I eat over there. Depachika items can really add up, and it isn't unusual for me to spend 3000 or more on a meat or chicken dish, some side dishes, maybe some bread from one of the many outstanding bakeries, a nice beer or two, and a fancy dessert. (And this doesn't even include fruit and cheese, which I usually pass by on account of the price.) I tend to eat lunch in restaurants but take dinner either in an izakaya or in my room.
As for the samples, when I first started going to Japan many years ago, they were a lot more common, and they were more often placed out in the open for easy taking. I have definitely noticed that this practice has become less widespread, in particular in the major tourist cities. I have heard it said that foreign tourists were the reason for this, although that could possibly be an overstatement. At any rate, I believe that many Japanese people would feel shame if they went around just taking samples of various items and not buying anything. I know I would. At any rate, nowadays the vendors are more likely to personally offer you a sample of something (rather than putting it out for anyone to take), and then they wait expectantly for you to react. I always feel awkward when I don't purchase anything after that, so I typically don't try a sample unless I am fairly interested in buying. The bottom line is that depachika samples are not intended as an all-you-can-eat free smorgasbord. It's more like "try before you buy."