20,000 yen fruit? Square Watermelons? Omiyage? Gift giving in Japan explained!

I remember taking this picture when I was out shopping soon after we'd first arrived in Japan, and thinking "what on Earth?!" when I did.
Firstly - has anyone ever seen a square watermelon before who hasn't been to Japan?
And secondly - have you ever seen watermelons going in the 10,000-20,000 yen range? (That's about $90-$180 US dollars, give or take a little bit depending on the exchange rate at the time).
I know I hadn't, and I guess that's why my jaw almost hit the floor when I saw these. I ended up having to ask my husband about the reasoning behind why gift giving expensive fruit is such a popular thing here. He lived in Japan for the better part of his childhood, being a quarter Japanese himself - and has studied Asian History for his Masters Degree. So I guess you could say that Japan, the culture and the history here are his passions in life.

The first thing he mentioned to me was that first and foremost, the concept of perishable gifts is popular here just due to the average housing size being smaller than what we're used to back in the US and Australia. Giving something that can be consumed is often a practicality thing - it's a whole lot easier if you're giving something that people can eat rather than something people need to store.
Case in point - just about everywhere you go in Japan will have adorably boxed "omiyage", (the closest literal translation based on the kanji is "product of the Earth"), which are often cookies, cakes or other food stuffs that are individually wrapped. Here's some I saw when I was at Fuji Q Highlands - Hello Kitty!!

Secondly, there's that idea of exclusivity. Limited edition gifts are popular here, so things like seasonal fruit with no imperfections, perfect in size, shape and color really fits the bill. You'll see in the melon picture at the top, they have zero blemishes, lovely coloring, they're perfectly shaped and so forth. You'll also often see other fruits that are gift boxed and far more expensive than your "regular" fruit, like gift boxed apples, peaches, rockmelons and more - and again they're all flawless and blemish free.
As for the mystery behind how they actually grow square watermelons, it's actually not all that mysterious at all! When the melon itself is still at a small size on the vine, a glass or solid plastic box is placed around the melon itself - and then it just ends up taking the shape of the box! Mystery solved!
Have you bought any food gifts/omiyage for people when you've been living or vacationing in Japan? Are there any particular favorites people have seemed to enjoy?