What is the context in which a species gets the name "elegans"
Since "meaningfulness" is not listed among the requirements for new names, any author is free in his choice of name derivation. [There are nevertheless some natural restrictions, such that new names are to be treated as Latin irrespective of the etymology and should follow Latin grammar (with botanical nomenclature being much more meticulous in this respect).]
There are indeed some cases when the name of the species may be meaningful for the purpose of the choice of type species (the "typicus/a/um" names and tautonomous names like "Glis glis"), but "elegans" doesn't belong here.


So, the high frequency of "elegans" has nothing to do with typification and reflects nothing else than the will of authors to reflect their emotions. One recurrent cause of "elegans"-names among paleontologists, for example, is good preservation of the respective fossil material. [By the way, there are even more emotionally loaded (but less frequent) names like "mirabilis/e" or "enigmatica/us/um".]

Since providing etymologies for names alongside formal descriptions of new species at a certain moment became an official recommendation, you can make your own collection of causes people provide to justify their choice of "elegans" as species names.

EDIT: I've just found this revelation: (Oxytomoides elegans, fossil bivalve) "Etymology. Elegans, Latin for choice or select, referring to what we regard as esthetically pleasing appearance of the species".