At the heart of the matter seems to be: should congress have to explicitly disallow the government from doing anything it wants? There is extensive legislation saying when companies like (or similar to) Apple need to comply with law enforcement. They are relatively new (the 90s). This means congress has considered the issue extensively, and ultimately decided to not force a company like Apple to comply with law enforcement in certain circumstances. The DOJ wants that to mean that they can still force them. However, the Judge is saying that, effectively, since the issue has been debated and congress has not forced companies Apple to help, this is a legislative choice, and thus being able to force Apple to help through the all writs act would violate the separation of powers.
Basically, if you believe the DOJ's line of thought, congress could decide not to pass a bill giving the courts the ability to do something, then the courts could still use the all writs act to give themselves that power. Because there is no law outlawing it.
That's not the question, though: the question is whether the All Writs Act already grants that power, or whether a new piece of legislation is required.
I think that Apple is right that it is more conservative for the courts to construe the existing legislation narrowly, since the Government always has the option to put specific legislation before Congress to remove all doubt.
It's precisely because it is a very broad law that it should be construed narrowly - in this case, that it is intended to be able to compel the co-operation of parties with some real involvement in a case, not to authorise open-ended civil conscription in service of the judicial branch.