Generally, I agree, and I’m a firm backer of pure research for the sake of research, and yes, lots of unexpected stuff comes out of it. But this “building a bigger atom” business doesn’t seem like research at all to me. It seems like trying to break a record (for largest house of cards, perhaps). Research usually tries to answer a question. The only question here is: can we? Answer: yes. Well, good for you! 
Well, one reason (and I’m sure there are several other perfectly valid ones) is that there’s the potential for something really interesting in those islands of stability farther up the atomic number scale. If there are elements stable long enough to be useful in practical applications, maybe they’ll have properties that are highly desirable.
To get there, though, you’ve got to take baby steps. Incremental advancement is the only way. So “can we?” becomes the stepping stone for the next “can we?”…and little by little we hopefully find ourselves somewhere very cool.
We think we partially understand the way the nucleus is structured, and how the energy levels in it work. Creating these super-heavy elements and watching them decay is one way to test our knowledge. We may not be able to use the super-heavy elements themselves for anything, but studying them gives us better understanding of the ones we can use, and who knows where that might lead?
Notwithstanding your (to me) sensible remarks, I’m wondering:
A very very long time ago someone had copper in one hand, tin in the other. In a 2001 moment, he threw them in a fire and smushed them together. Voila.
So, question: we have a ton of elements. Which ones (based on criteria of your choosing) can we still say “it has no uses”?
As Secretary Rumsfeld put it, there are “no uses” and “no uses.” Let’s put one of the end points of the answers to my question as the “no uses” of ununseptium.
WebElements has a section for the practical uses for each element. You’d have to go through them one at a time, but from a quick skim, it looks like berkelium (97) might be the lowest-numbered element without any uses listed.
Thanks.
Poor Berkelium. 
The first of the useless ones.
But perhaps the stone rejected will become the capstone. [CMLeo Bloom]
Eventually has gotten closer. And even better is this stuff–Z-113, Z-115, Z-117, and Z-18, is now officially “stuff.” Plus that Periodic Table looks a lot less sloppy.
From the International Union of Pure and Applied Chemistry:
…The proposed names and symbols will be checked by the Inorganic Chemistry Division of IUPAC for consistency, translatability into other languages, possible prior historic use for other cases, etc. New elements can be named after a mythological concept, a mineral, a place or country, a property or a scientist (see: W.H. Koppenol, PAC 74 (2002) 787-791). After Divisional acceptance, the names and two-letter symbols will be presented for public review for five months, before the highest body of IUPAC, the Council, will make a final decision on the names of these new chemical elements and their two-letter symbols and their introduction into the Periodic Table of the Elements…
Well, it’s named after Berkeley, California, so I’d say that’s pretty appropriate 
Honestly, I think the chance to name an element is the main prize. Superheavy elements don’t last long enough for us to even study them, much less find uses. Creating one is like being the first person to discover a new planet. It’ll probably never be “useful,” but it’s damn cool.
I think “unobtainium” counts as a “mythological concept”, no?
I can’t believe I’m responding to the OP in a zombie thread, but in case anyone else is wondering…
Why were 116 and 118 found first? Nuclei love even numbers. Even number of protons, even number of neutrons.
OP-Zombie/Zombie-OP
All four of us.
It is at least useful to get some data about the actual half-life so that we can compare real-world results with predictions made by our models. A big discrepancy might highlight an unknown factor we need to research more closely.
Not that six atoms is going to provide a useful sample for that purpose, though…
Well, that’s its use then - to be the answer to the question ‘what is the lightest useless element?’
This reminds me of that old “lowest uninteresting number” proof.
Which is quite easily explained by the fact that protons and neutrons have two spin states. Take an even-even nucleus, and add one more particle. If there’s room for that one, then there’s also room for another one in the same state except opposite spin, and now you’re back to even-even again.
Of course, some even numbers will be more stable than others, due to the complex intricacies of the nuclear force and the quantum mechanical state, but you can at least be sure that two of each will be stable.
Incidentally, this exact same reasoning also applies to electrons, which is why helium is extraordinarily stable in both nuclear and standard chemistry: It’s got two of each kind of particle, all in their ground states, one each spin up and spin down.
Oh, and the lowest uninteresting number is 1.
Exactly what I had been thinking!
So how many garbage trucks of flaming grant money did this discovery cost?
It is also the loneliest number…
Any reason to expect that powers of two would be extra-stable? 2, 4, 8, 16, 32, etc. If so, that might imply that element 128 might be worth searching for if we want something that doesn’t immediately fizzle?