An embedded system is built to be specific to its task using minimal software/hardware to achieve maximum reliability, minimal cost, and minimal physical size. Think network appliance not computer server. One of the outcomes is that a Compact Flash (CF) drive is used instead of a hard drive.
There are a number of advantages to using CF. It has no moving parts, no spin up time, uses much less power than hard drives, generates almost no heat, is physically very small, and makes no noise. Hard drives are particularly vulnerable to corruption during power failure. You can use a RAID array and a UPS to improve reliability but that adds cost, increased power requirements, more heat generation, more noise and increased physical space requirements.
Because of the lower power requirements and minimal heat generation with CF, a small fan less ATX power supply or low cost power brick with DC output may be an option. You would also need a suitable motherboard with DC input or DC converter to plug into a standard ATX motherboard connector. While we are at it, choosing a CPU that does not require a fan is preferable assuming you are not doing a lot of CPU intensive tasks such as transcoding, software echo cancellation, and multiple simultaneous calls. A fan is just another thing that can and does fail not to mention the fact it adds noise. Of course, there is nothing stopping you from using just about any old PC you may have sitting around, at least for experimenting.