As previous posters mentioned, your ward clerk chose one of two options, or didn't know there was any difference. I'd guess the latter. They probably did it that way before lds.org directory came about.
When ward clerk, (with a wife that was primary president) I didn't see the value in having a long list of generic "primary workers," either. We chose to change to the more specific callings, such as "primary worker - CTR 8," etc. These are still standard callings...don't make any custom callings!
As noted by davesudweeks, doing so is not without technical problems, especially around the start of each new year, as assignments change. Choosing either method doesn't really change the fact that you're "called" as a primary worker in the Primary organization, and "assigned" to teach a certain class within that organization. So, other than making the ward clerk do some extra work, you are not asking for a significant change from your ward leadership.
If you make the change: Make sure you print a listing of everyone's "sustained" dates and "set-apart" status before "releasing" and "re-calling" each worker with-in MLS, so you can use the same sustained date.
"A soft answer turneth away wrath" works great on LDSTech forum boards!