Why do pilots say "clear of the active" at non-towered airports?
Honestly? It's probably because they heard someone else do it, and thought it sounded cool (or otherwise just got it stuck in their head).

You're 100% right - saying the runway name is, if slightly longer, certainly a bit more informative. It's the kind of thing that can help arriving pilots know which runway is in use, keeping later radio clutter ("Um, uhh, Jeffco Traffic, um, say runway in use?") to a minimum for pilots already on frequency. Even a 'one runway airport' still has two runways (09/27, for example), and it's nice to know which one you should set up for when winds are light.

The preferred terminology is more like "Jeffco Traffic, 3AC, clear 29".