This article may have some info you can use.
http://www.tekrevue.com/tip/ins-outs-imacs-target-display-mode/
Here's the thing - your iMac has a Thunderbolt port. Does the PC also have a Thunderbolt port, or MiniDisplayPort? That's key to the incompatibility.
"Why, Apple?" Are you questioning why they moved to Thunderbolt, which is a port with a whole lot more capabilities than MiniDisplayPort? Should they have stuck with MiniDisplayPort just for the sake of TDM? Should they have continued with separate ports for data and displays (and the separate controllers to go along with them)? Still, I don't know why this is "unspeakably frustrating." There are pros and cons to nearly every design decision, and I've yet to see any computer that combines every feature and capability that exist. Generally, little-used features are going to get pared away in favor of more broadly useful features. This particular capability was "universal" on iMacs for just three years, in the entire history of iMac. For two years prior to that, it was possible only on the 27" iMacs. Before that, nada. After that, nada. A brief window that was nice while it lasted.