I took it not so much that the increased thought leads to more useful phrases, but that people are more likely to exert this effort toward things they think are useful, rather than lies.

You are going to remember "righty-tighty, lefty-loosey" better than "blue shoe, red bed" because you think it more useful. And you are vastly more likely to put effort into teaching the former to others.

When designing rhymes less for your own benefit and more for others, like advertising slogans, this obviously doesn't hold as well.