But pi isn't a slice of pie – it's half a pie, right?

But half a pie is a slice of pie, right?

But pi links to diameter, not radius.

A slice has two sides. 2*r = d.

That's wordplay, not mathematical content. You're actually taking students farther from understanding with that.

You really can't overestimate what can block up a student with this stuff.

Exactly. It's much a "stickier"/"easier" mnemonic to tell a(n English-speaking) grade-school student "the area of a circle is 'pi r squared'" and let them giggle at the incongruity of the fact that no, silly, pie is round!

It builds a connection to a thing they already know, and it's "silly"/"absurd" enough to be "sticky" in terms of memorization.