Nothing falls afoul of thermodynamics. This is not a closed system - you can inject as much energy into as you have available. Entropy and thermodynamics play no role here, but I would imagine that (a) the cost of the energy require (b) containment technology (c) what happens after you extract a given substance are/were all very involved in its failure.

This is already done with crude oil, and is called "cat cracking". You heat the crude oil until every component in it becomes gaseous (but still small-molecule) - the smaller the molecules they higher they rise up the "chimney", so you can siphon off particular components at particular heights.

I wasn't arguing that it is impossible, which as you say, is only true in a closed system. What I was saying was that since you wasted the organisation of the system, sorting it out again is going to take more energy than if you didn't. I think that's a consequence of the fact that you increased the entropy.