If these kind of entities actually want to preserve resources, they shouldn't be generating a petabyte of bandwidth charges. Contact soundcloud and come to an agreement that will be responsible.
How much does a petabyte of bandwidth go for these days anyway? It might as well be cheaper than paying engineering, legal and management to arrange for some kind of off-line data transfer.
Or if you worked with them, and both of you happened to be in Amazon, that could be a no-cost transfer.
I expect they, like any business, would take a stance primarily based on liability, cost, benefit, etc... overriding how anyone working at the company actually feels about it.
It costs them nothing to ignore/outright reject without consideration a crazy proposal like "lets give our entire database of content to a third party". Assessing the technical and legal ramifications of that proposal costs time/effort/money. Why bother?
If SoundCloud gives their content to Archive Team, they're shouldering the possibility of some kind of liability, surely. If they say nothing, let Archive Team take it themselves, from their website, they let Archive Team (who understand and are willing to) take responsibility for that.
This way they can skate the rules and save the data.
Plus startups on the way out usually want to use their data as a bargaining chip to sell whatever remains of the service off, if they give it away they lose that chip.