It's not like building a website. You need serious funding for hardware. You need people to manage the hardware. You need complex software to manage the data and ensure security. One serious breach early on and you're done.
Competing with Amazon is especially hard since S3 is well established and entrenched. If you use EC2 you're going to use S3.
Pricing would be a primary factor in competing. 3x redundancy is unnecessary. I'm not sure why services still do that. Reed-Solomon or similar redundancy algorithms can provide better protection and use less space. They have CPU overhead but CPUs aren't going to be the bottleneck for a storage service, bandwidth and hard drives will be.
Edit: This would be if you built from the hardware up. I don't think offering a service like S3 on top of other storage services would work as a business. You'd have to deal with too many vendors, too much variation in APIs / software / hardware, lack of control, latency issues, and much tighter margins. IMO you'd be better off starting with bare metal. You could do something like this for personal, smaller scale storage but growing it to scale would be a nightmare.