There is a valid case for "powerful" home servers. Centrally backing up all the PCs in the house and streaming media to computers/TVs/consoles/tablets are two things I do in my house with my server. Granted it's not a brand new system, but it's a Core 2 Quad with 8GB of RAM, 20TB of hard drive space, and a Radeon 5700. Streaming and storing HD video isn't cheap. This centralized server is more cost-effective and convenient than all of my roommates having the media stored locally, though.
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.
