The short answer is: yes, if it is not on an enterprise site.
I have hosted numerous servers on old desktop hardware, there is nothing wrong with this. Old computers can make excellent file, Minecraft, and web servers. However, if you are honestly asking the question “should you run a server on desktop hardware” it implies you are running something important. Don’t get me wrong, running a Minecraft server is very important, however, it is not as important as a production web server for a larger company. In that case it is better to have an actual server with redundant power supplies and hot swappable hard drives.
Many people don’t realize that the slowest part of their computer is the hard drive. The read and write speeds of a hard drive affects the computer’s performance. The most affected processes are the boot time and time it takes to open an application.
I decided to explore the speed differences between several types of hard drives. In all the trials I used a program called Parkdale for speed measurements. *Please note that these are just the hard drives I had lying around, there can be great variation of performances between different manufacturers.