I've been reading up on R. Smullyan's "To Mock a Mockingbird" and Hindley's "Lambda-Calculus and Combinators: An Introduction". I've even read Schonfinkel's 1924 paper introducing the idea of combinators and followed up with some Curry. "After" reading Hindley I can say that I "get" CL to some extent (and perhaps is the reason for this question).
However, CL seems to be presented in the language of $\lambda$-calculus. This seems to have been a general progression AFAIK where $\lambda$ superseded CL and the latter seems to have fallen off to the wayside.
My understanding is that although one can "define" a combinator like so in CL, the only way to "implement" it is via $\lambda$? Is this a valid inference? A satisfactory mathematical definition of a combinator may not be possible and thus it's described in the language of $\lambda$ and thus it's not relevant by itself per se.
The "concept" of combinators may still be useful (although I can't yet say how/where) for gaining some insight owing to it being "variable free" but for the most part it seems irrelevant as of today (2019-20). Almost everything in CL can be translated to $\lambda$ and vice versa. So is there any "insight" to be gained by studying CL? Is it now just a "simpler alternative" than $\lambda$ when trying to understand something that could get messy when analyzing with $\lambda$? Or is there more to it than meets the eye?
Is my understanding/assumption correct? What are the other reasons for it to not be "mainstream PLT" (or is that just my POV)?