While I wouldn't call this scummy I do agree with your sentiment. It is technically stealing and those copyrights should be respected.

Full disclosure, I am a career musician AND have been known to pirate material. That said, I think this is a valuable archive to build. There are a lot of recordings that will not endure without some kind of archiving. So while it's not a perfect solution, I do think it has an important role to play in preservation for future generations.

Perhaps it's best to have a light barrier to entry. Something like "Yes, you can listen to these records, but it should be in the spirit of requesting the material for review, and not just as a no-pay alternative to listening on Spotify." Give it just enough friction where people would rather pay the $12/month to use a streaming service.

Also, it's not like streaming services are a lucrative source of income for most artists. I expect the small amount of revenue lost to listeners of Anna's Archive are just (fractions of) a penny in the bucket of any income that a serious artist would stand to make.