So you should factor in the bandwidth cost for CDN traffic AND origin pulls, which if you're serving from AWS (and not using CloudFront), is $0.08/GB.
The size of your working set also influences your overall CDN bill. Storage isn't free.
The storage cost is a good point, and I don't know which CDN they use, but I expect the songs that weren't "hot" would be evicted from edge caches pretty fast, so that should be no significant increase.
To put things into perspective, an article from 2009 estimates that Spotify used 84TB of traffic per day[1], back when they had 5 million users. Soundcloud claims to have had 40 million registered users in 2013 and 175 million unique monthly listeners in 2014. These numbers aren't easy to compare, but either way I think it's safe to say that 900TB should be a small fraction of their monthly traffic, and shouldn't make a huge dent in their financials.
[1]: https://www.theguardian.com/technology/blog/2009/oct/08/spot...
Why stay with a host that bends you over a barrel for transit? Even Netflix doesn't use Amazon to deliver their data heavy content, as their pricing is pie in the sky high.
Obviously, there's more than just the bandwidth cost, but assuming they pay $0.02/GB for CDN traffic, we're talking about $18k. It's not nothing, but I doubt it'd change their outlook in any meaningful way.
I should add that the ArchiveTeam doesn't download everything in a day, but rather uses a distributed crawler (ArchiveTeam Warrior) run by volunteers. They rate-limit the crawling rate as needed in order not to overwhelm the site being archived.