Seems as though I have to give my members the Architect role to do this – which simultaneously gives them database access to the space, which is not desirable. Yet, as Owners have the ability to delete documents. 
Just seems odd to be able to delete documents as an Owner but not move docs or create folders.
Am I using roles incorrectly?
Your understanding is correct: Owners cannot create folders or move docs.
However, we plan to make it possible for someone to be a space Architect (allowing them to create folders, move docs, as well as add data views to the sidebar) without granting them access to the databases in the space, which I guess may cover the use case you have in mind (?)