I wonder what you would accept as "empirical evidence" of the relative ease of rhyming in different languages. The demand strikes me as typifying one of the obnoxious impulses of the Hacker News community (another of them on display elsewhere in this thread) to dress up a vapid criticism as scientific skepticism.
You could, I suppose, try to do a combinatorial analysis of the ease of rhyming by writing a program to find rhyming pairs in a phonetic dictionary; just make sure your blog post about the results properly acknowledges the shortcomings of your analysis in its title.
0. https://books.google.com/books?id=ByVoAgAAQBAJ&lpg=PA60&ots=...