You don't need need memory or CPU power for streaming or backups, unless you are doing on the fly transcoding. You do need storage connectivity but even USB2 has a theoretical throughput of 60 megabytes per second while you'll get practical throughput of ~35 megabytes per second on gigabit ethernet.
The only time I saw my ~2005 era system have non-trivial CPU usage was when doing encryption, and even then it would peak at around 25% of CPU.
Encryption and compression are what the CPU and memory are for. The video card is for transcoding to deliver to the target system. It's mainly just a re-used system, but you wouldn't be able to do it with a PII and 64MB of RAM.
The only time I saw my ~2005 era system have non-trivial CPU usage was when doing encryption, and even then it would peak at around 25% of CPU.