I enjoyed Gillian Beer's article "The End of the Line" from The Guardian.
Beer uses the awful word "suggest" to make her claim; I would say that she "points out" that rhyme has two effects beyond helping us memorize: "rhyme makes experience from within the body and so can produce unreasoned intimacy; rhyme destabilises the hierarchies of sense and so lends itself to radicalism."
She goes on to argue that rhyme is "retrospective": "It is not until the second term appears, and it draws us back to what has gone before with a new thrill of connection. Thereafter it is janus-faced, leading the eye and particularly the ear forward to seek the chime, but with a ballast of sonorities generated in the poem's past. Rhyme makes memory within the poem. It practises recollection. It may also bring things back, uncannily changed."
Rhyme also serves to establish one of the basic facts of poetry: it functions "not as argument, but as experience - whether as fulfilment or entrapment - vouched for by the human ear."
But perhaps her finest point has to do with the "essentially destabilising" quality of rhyme, which she discusses near the end of her article: rhyme's arbitrariness, of course, but also its disregard for the niceties of language that are captured in the linguistic concept of "register."