Eliot himself explains in no uncertain terms in his seminal essay "Tradition and the Individual Talent" that what he intended to accomplish, and views as essent

Eliot himself explains in no uncertain terms in his seminal essay "Tradition and the Individual Talent" that what he intended to accomplish, and views as essential to the poetic form, resides in the referential nature of poetry to the past or "tradition", and the poet is a mere conduit or at best a curator of material that already exist. Although it's arguable that even he himself did not follow this dogmatic way of constructing poetry, his thesis effectively defined modernist literary criticism for decades. In that vein, it's not unreasonable, but also not top-of-mind, to connect his works and purported ethos to crosswords, as crosswords are necessarily referential but it had the flaw that it was not necessarily consisted of expressions of emotion and art via channeling tradition in a newly curated manner but rather, the expression of another, more "pop" form of culture that existed at the time. The connection between him and crosswords may very well be a product of the immense popularity of the crossword during his early adulthood when it was viewed as an almost transgressive element in society that, among other things, served as the convenient conduit du jour for mixed-gender interaction in social settings set up by clubs dedicated to these puzzles. But I really consider Eliot the first poet who openly advocated for what we'd consider "sampling" or "mashups". Although actual tech that could be used to sample music wouldn't exist until 30 years after Eliot first expressed his sentiments, and musical quotation certainly have existed before that, musical quotations are seldom directly acknowledged and never formed as the basis of a work in its entirety. Eliot did not necessarily quote verbatim every reference he made, but he made extensive footnotes directing to the source in many cases and in other cases used references to works popular enough that notation would not be needed. I very much think that what was being expressed by his works, starting with Prufrock but really peaking before the Four Quartets, is an attempt at legitimizing a way of creating art that served as a precursor for hip-hop and electronic music today.