> voluntarily
In the US, that is currently where we've drawn the line.
They can cooperate, but it has to be voluntarily and the private party can't be government-by-another-name (e.g. not NCMEC which has a special legislative permission to handle child porn and is overwhelmingly funded by the government), but an actual private party.
There's a difference between cops paying someone to break into a suspect's house to steal evidence without a warrant, and a 3rd party that, while doing business, comes across material that might be criminal evidence.
The former case, in the US, falls under the doctrine of the "fruit of the poisonous tree"[1]. Evidence collected illicitly won't be allowed in court, and any evidence or argument based on the tainted evidence can be thrown out, as well.
I think the line is blurred with the system in the OP, where it seems like it kind of fits the latter case. It's fuzzy to me when parties are working in tandem with law enforcement, even going as far as running law enforcement's own systems voluntarily, or collecting or giving up information without a warrant when simply asked. To me, that seems a lot more like former case, where the government persuades someone to collect evidence on their behalf without warrants or subpoenas.
[1] https://en.wikipedia.org/wiki/Fruit_of_the_poisonous_tree