Well, since you’re still taking in atmospheric carbon, including radioactive carbon, if they did, they’d get an age of “zero” within a certain error range.
The good news is that they can work with a fairly small sample; no need to take a pound of flesh.
I’ve noticed this before - indeed, creationism is riddled with such contradictions, although this is one of the most obvious.
It’s evidence that creationism isn’t even trying to be a coherent theory - it’s just a loose collection of arguments and criticisms that individually attempt to assault assorted pieces of existing science.
This fragmented nature is one of the things that makes creationism so persistent - it does not encourage, in its subscribers, a notion that problems should be resolved - instead, you just move to the next compartment and keep going.