"I've only ever had one student who came close to capturing what is really wrong with Cats. She focused on the fact that Andrew Lloyd Webber stuck too close to the original T.S. Eliot poems, which are mostly written in the third person. As a result, we rarely hear any of the cats singing about themselves, rather we hear about them from a third party. So, we never develop a bond with anyone on-stage, with the exception of Grizabella, who sings one of the few songs in the show that wasn't based directly on one of Eliot's poems. Pretty savvy, huh?"
This is not im-paws-able. But allow me to throw my penny into the kitty.
I'm not sure that this third person thing is the problem. Cats is a series of character portraits, not characters. As such we're not being asked to develop a bond with the characters so much as delight in the imagination that's portraying them. We're not bonding with the kitties; we're bonding with the whimsical mind of TS Eliot.
If Cats has a problem then it's more to do with the straight-jacketing effect of the light verse which sometimes forces the music into a predictable tum-ti-tum-ti-tum pattern. Sometimes Lord Andy can overcome this problem with inventive little bits of rhythm (as in the phrase: "The Rum Tum Tugger is a curious cat"). But the verse still doesn't quite offer the flexibility of an original lyric.
Even so, it's still a very entertaining miaow-sical.