Yes, as you gathered, the reviewer definitely doesn't like the song. My interpretation is as follows:
The "teased and coiffed" element relates to an overworked hairstyle. This later ties into the words "My Little Pony...." referring to the plastic horses for children in various colours with long bright, and false, "nylon" hair.
"monument": If you were being kind you might interpret this as meaning his legacy to the world. If you were being very harsh you could take it to mean his tombstone.
Others may have other views, but that's how it appears to me at present.
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