Because of the existence of free variables in lambda calculus, the evaluation of open terms (at least as outlined here) is more complicated relative to the evaluation of closed terms since the evaluator must ensure that the beta-reduction step uses capture-avoiding substitution, i.e., that the variables it substitutes into a term are not free variables of that term.
Combinatory logic can be seen as a subset of lambda calculus that only allows closed terms. Despite this, it is still Turing-complete, and can thus be used to compute everything that lambda calculus can. As such, what are the benefits of allowing free variables and open terms, and the disadvantages of disallowing them? On a related note, why does lambda calculus seem to be a more popular topic of study than combinatory logic despite the apparent shortcoming mentioned? Is the former somehow more relevant and useful to a larger variety of topics than the latter?