And our duty as a flying instructors is to ensure that we teach in accordance with the a/c manual.
Cessna & Piper both specify that the primer is to be locked prior to take-off. Not one of their inflight procedures specifies the use of the primer with the possible exception of an inflight restart. Don't have access to a manual to check...
Cat, to answer your (unspoken) query. No, I'm not now an instructor. I last instructed in 1999, having instructed since 1989. My instructing experience ranged from aero club to airline college; PPL, CPL, IR, night, multi, instructor, aeros and CFI positions for schools that taught these. There were also a few test approvals that came with the CFI jobs.