That's a super interesting question. Pretty much the entire challenge of LC is coming to understand why it's interesting. From our perspective, so far past the consequences of this discovery, it will all seem too obvious to state. The interestingness of LC comes out of it being so austere and so powerful.
Frankly, this page's intro to it is sort of terrible. Clojure is too powerful and clunky to point directly at LC and show why it's interesting.
LC is a language with three constructors
var[x] reference a name
lam[x](...) create a scope where x is *known*
app(f, v) when f is lam[x], give
meaning to x within its body
app(lam[x](body), value) ==> body{x -> value}
So imagine that to be the definition of a programming language---the whole thing. It seems a bit silly. It doesn't obviously have any of
- numbers
- if-the-else
- for loops
- recursion
- mutation
- data types
So the magic, of course, is that it actually does have all of the above. Those 3 constructors and one rule are powerful enough already to generate all of that.
That's what's remarkable.
However, if you want to do research, it is an invaluable model of how computation works. It's simplicity allows for reasoning about complex ideas while minimizing the cognitive overhead of the model.
It may also help you understand why certain functional styles behave the way they do or how to better implement programming languages.
If none of those things interest you, then yes, it is not useful. But a large crowd here IS interested in computer science theory and programming language theory and functional programming so they are interested.
As a final analogy, you might consider this the 'Standard Model' of computation much like there is the Standard Model in particle physics. If you are a civil engineer, it will never be useful. If you are a chemist, it might be useful only in passing. But if you are the physicist, it is invaluable.