That's what the main point of The Problem with Carbon 14 and other dating methods
is about:
They know, that carbon dating won't give meaningful results for samples which are older than ~50,000 years. They do it non the less. And they do it again. And they claim that they have proved either that the world is less than 50,000 years old or that carbon dating doesn't work.
To get back to our little analogy: this is like claiming that their is either less than one litre of liquid or that it is impossible to measure the amount of one gallon...
Thats not the only problems to carbon dating!