Isn't a 24-word seed phrase overkill? Is 12 words fine?

Just got my first Ledger, and it defaults to a 24-word seed phrase.

AFAIK, it would take a trillion computers, guessing a trillion times a second, for the lifetime of the universe, to brute-force a 12-word seed phrase. A 24-word seed phrase seems like overkill.

While I will be carefully storing my seed phrase, I also plan on committing it to memory. I have some experience with this, and 12 words is doable. But I'm not so sure about 24 words.

I'm considering making a 12-word seed phrase wallet, and restoring the Ledger from that.

So, is a 24-word seed phrase overkill? Is 12 words fine? Is there something I'm not thinking about?