Funny, i can't think of anything MORE exciting and awesome . However, i think the main point is that when you're faced with overcrowding on a planetary scale, with 10s of billions of people, the idea of free "wide open spaces" living isn't feasable, and arcologies are one of the best alternatives. Not to mention they look uber cool and they're super futuristic.
actually i must respectfully disagree. the entire 6+ billion people on earth, if we were to stand shoulder-to-shoulder, would occupy the space of Rhode Island. in 4-person suburban-style homes, we'd take up a space the size of Texas.
over-crowding is really an issue of providing lives for so many people, not just space. food, clothes, possibly even personal transportation and entertainment. no real proposed arcology or mega-structure of any sort has meant to be completely self-contained. they still need food, air, power, and information from the outside world. food and air would be the hardest challenges, as shown by the failure of Biosphere 2.
however, arcologies do solve, or at least address, some of our over-population problems. it curbs suburbanization obviously, and with it the need to provide personal transportation to people. in that pyrimid-shaped design above, those links that connect the buildings are actually like subway tubes. transporting needed resources is also a bit easier, since you really only have one destination. given a bit of technological advancement, power shouldn't be an issue, and information can obviously be made lightweight (literally... anyone get that?). arcologies, it seems to me, can make more efficient use of consumed resources (distributing resources in a pre-organized and contained area the size of downtown LA would be a lot easier than a haphazardly-developed LA county with its malignant suburbs). it can also potentially mean we use less arable land for living on, and more for growing on. and if the environment were more hostile to us, it'd make coping with that a lot easier.
but sorry i lost track of my point. "wide open living" is unfeasible, not because of the raw number of humans, but because of out subsequent needs. arcologies in and of themselves would have a marginal effect on that at best, plus represent considerable resource expendatures in themselves. Star Trek -like technologies, such as anti-matter power generation and food replication, on the other hand, would allow us to spread out to a population 10 or 20 times what we have now before the wide open spaces were totally gone.