Think back to how much of your western education was spent on completely pointless exercises...

That's certainly true, but at the same time I rarely spent much time at home on schoolwork either.

It wouldn't be that hard - 3 year olds commonly memorize entire songs and rhymes they hear.

You just put the numbers to music or make a rhyme - how much you want to bet there is a little industry making CD's for this?

But it is totally pointless. Learning to memorize stuff is useful, but learning to memorize a single thing isn't.

Its definitely a culture thing. Its best shown by the Chinese parent's desire for their kids to play the piano.

Do you think Chinese parents make their kids learn piano because they themselves were inspired by Mozart and Chopin? No, they learn piano because it is something that the kid can show off (to relatives, colleges, etc).

Those kids learn PI much in the same way.

Are you referring to Chinese immigrants? Because if China is anything like India, kids would actually be discouraged to play the piano, as it would prove to be a "distraction from their studies."