Large companies on the other hand need to have the reliability and security of a big name behind the storage. Why would they even consider moving to a no-name company that hasn't proven itself? Sorry, it just seems like the wrong niche to step in to.
I'd like to use DigitalOcean or Linode VPS machines for processing and as web servers, but then I need a large object store like S3. Rackspace and AWS have both object storage and VPS, but their VPS machines are underpowered for the price.
So ideally I would use Rackspace-Files or Amazon-S3 for storage, and DigitalOcean for number crunching, but I'd get killed on transfer rates from S3 to DigitalOcean (for example). Amazon and Rackspace have a trump card with free data transfer within their data centers. You have to use their slow machines to realistically use their object stores in this type of a use case.
So that's the 'S3' problem I need solved, which still isn't quite what S3ForMe is going after. Extremely cheap data transfers to/from major VPS providers.
Back to pgrove's point, though — there are trade offs with using a dedicated server. The storage isn't as reliable as S3 and the server itself is likely less reliable than a VPS (since some hardware problems on a VPS can be solved by migrating to new hardware and only involve a small downtime, rather than the large downtime of restoring from backup).
A major advantage to dedicated servers that I don't hear much about is simplicity. Dropping everything on a dedicated server means I can use local services like the file system rather than having to deal with S3 and latency and bandwidth costs.
Edit: I just realized that the idea was to use Rackspace files + one of their servers rather than S3 + EC2. Somehow I missed that bit and was thinking about just storing everything on the dedicated server.