That would help but the cost of storage for 11 TB and the up time to download would be extremely expensive. I haven't seen an option that works for less than around $200 to rent and setup.
It seems like if these large public datasets continue to come on line, there will need to be some sort of semi-cooperative distributed data store to make them truly "accessible." Or the data provider will need to provide an access/query API, rather than just a big tank that you can copy if you dare.