I don't think it's the same situation, since there's a rough baseline rate of carbon-14 in nature (relative to carbon-12) which is continually replenished while

I don't think it's the same situation, since there's a rough baseline rate of carbon-14 in nature (relative to carbon-12) which is continually replenished while alive. When it dies, there's no more carbon-14 added to the system, so we can determine how much is "left" from the ratio of carbon-14 to carbon-12. But there was no fixed % of ceaseium-137 to start with here, so we can't use the current % to determine age.