It's unlikely that the Fourth Earl of Sandwich, who lent his name to the snack, ever went for the cucumber option. The Earl wanted something tidily substantial to refresh his efforts at the card table, not some prissy confection.
No, the cucumber sandwich was made to be part of English afternoon tea, which, in that subtly snobbish English way, was designed to demonstrate that you were able to indulge in a meal for show rather than sustenance.
Both Dickens and Wilde were alert to this sandwich symbolism: Boz enjoyed the small triangular ones at the finishing school run by the Misses Crumpton in Hammersmith, and Oscar teased with Lady Bracknell's. But, also in the English way, the CS can triumph over its origins, and provoke fond memories of summer days and shaded pavilions.
Some may wonder why the cucumber was chosen for this crucial social role, especially when many people find it indigestible. But that's exactly why: you need a strong stomach for the upper crust.