I don't see why you'd reject a sample just for not being full, that seems a bit unnecessary. QNS or a short sample, obviously, but most patients come through for their T/S, the screen is negative, and that's it. If you had to wait for a new sample, their old sample could have been done by then. Additionally, calling for "fuller tubes" isn't really the way to ensure higher quality in patient care.
Overall, not worth the effort. The care teams on the floor are already quite unhappy when they have to redraw for other reasons, I can't imagine what they'd say if I called requiring a completely full sample! Their fragile stick patients may not be happy either...