The packaging for Stabilicers warns explicitly not to use them on rock, if memory serves. If there isn't an ice substrate to bite into, then reducing the areal contact between foot and rock, by switching from boot sole to Stabilicer edges, is a poor idea friction-wise, methinks.
OTOH, Stablicers are a boon when 'whackin' through the woods in winter, in addition to their customary uses on verglas, etc. You wouldn't want to be on crampons on top of loose snow on top of icy/wet wood and leaves. However, the Stabilicers are pretty slick for this purpose. (Yes, the perverse pun IS intended.)
I tried last winter to get a discussion going on tricounis, but no one seemed to get the point. Okay, okay, I'll go sit in my pun-free corner now ....