Just because those new elements are pretty much useless with current technology doesn't mean they'll be useless forever. 
They are not a "new" element though.
They are just an alloy. They take a bunch of other elements, shove it together, and call it a new element. The fact that it quickly breaks down into a base element means that they are not true elements. They would be 100% stable on their own, rather then needing to be made in a lab, and lasting just a few seconds.
Eventually we will just have 10,000 elements and the chemistry final will be complete and utter hell.
Nobody knows for sure but I'd guess it's finite because there's only a certain amount of protons you can pump in until an atom becomes very unstable.
If this is any example, then there is an infinite number of elements. All we have to do is make it stick together for just a little while, and we can call it a new element. Eventually we will invent statis fields and just push a bunch of particles together and put a check on the clipboard and then push another one in.
In that respect, I guess these types of discoveries are useful. We can't really know where to develop if we don't know what direction we are headed in. I just wish the process were a little more mysterious and natural. To me it feels less like we are discovering the universe and more like we are creating it.
The best way to learn something, is to honestly build it, or take it apart (and put it back together).
When I first learned about computers, to understand cpu's and ram and all of that shit. I built a computer. It showed me each and every component, how they tie together, and what happens when something is missing. I know much more about how they work, because I built it, and make it work from scratch.
When I first learned how to program, I read a tutorial on it, and then built my own program. Actually typing out the structure, and seeing how its built step by step, showed me exactly what I needed to know to program in the future, and got me started right away on building bigger and more complicated programs.
Building new elements is awesome. But stop calling it an element until its actually a fucking element, not two elements stuck together by glue that's going to break any second. When an element can contain its electrons and neutrons, then it actually becomes an element. Until then, its a pile of neutrons and electrons.