Just personal observation, maybe it feels different for a professional English song lyric composer.
I don’t have a spreadsheet, but so many characters have the same ending sounds in Mandarin that I could easily find a rhyming word when writing song lyrics.
English is a struggle to find a rhyming word that fits into the context of the contents, and it feels kinda like a forced rhyme.
I haven’t really spoken Mandarin for over 15 years, somehow it’s still easier to do rhyming.
P.S. Cantonese has more variety of sounds and less characters have the same ending sounds, so its harder to rhyme in Cantonese.
Other replies answered what’s what. I think the reasoning for this many names is just there are many variants. After all, the current “nation” is several ethnic groups (many with their own languages) merged together for over thousands of years, spanning a large area.