Yes, it's ignorant to talk about a carbon-free economy. Who has said such a thing?
The term typically used is "carbon-constrained". And it's quite clearly understood to apply to the rate at which we release locked-up carbon into the atmosphere, largely by burning fossil fuels.
The earth's ecosystem is capable of absorbing it at a particular rate, and clearly it would be nonsense to think we can keep releasing it at a rate faster than this (unless we were to attempt artificially boosting the absorbtion rate, but there are good reasons to assume that this will cost more energy that simply releasing it more slowly in the first place).