I agree that they'd try to help if they could but I think we'd have to assume that getting someone plugged back into the Matrix permanently would carry a much greater risk for the crew required to carry out this operation than is acceptable.

I think this assumption is reasonable because:

1. When Neo leaves the matrix, within a minute of "waking up" a machine quickly arrives to unscrew his neural connection and flush him down the waste disposal at the back of the pod he was "asleep" in. So we can assume that there's constant monitoring of the pods and lots of machines to quickly dispose of humans that wake up.

2. The humans want to stay as far away from the machines as possible, hence why they use a dish to broadcast a signal from a hidden portion of the world outside of Zion so they can jack into the Matrix remotely and disconnect when they need to move to avoid detection. Getting inside of one of these human pod farms likely would be a nigh-on impossible task as can be seen when A. Neo and Trinity fly into the heart of machine territory in the 3rd film and B. Morpheus and the crew wait until after Neo gets flushed out into what most of the time is a corpse sewer to fish him out.

3. During the whole explanation of the matrix from Morpheus we can see that as soon as a human is grown enough to be picked they're moved into one of these pods. So even if they somehow manage to sneak into one of these facilities without being detected by one of the innumerable monitoring machines they'd either need to A. Time it perfectly between a dead person being flushed out before the pod is repopulated with a new young person from the farms. Or B. Swap Cypher in when someone else wants to come out, when they state in the film that spending enough time in the Matrix to extract someone is already a risky operation.

4. They might not be rule tyrants but Zion clearly has a leadership hierarchy and risking a whole crew and a ship which has information on how to find and get into Zion in it's systems would likely be a completely unacceptable risk to Zion management who already don't like Morpheus' recklessness for chasing the prophecy by freeing Neo in his 20s when they normally only free people when they're younger.