There is plenty of time to view checklists when you fly multi-crew, for single pilot operation you need to fly the aeroplane first.
I am trying to think of situations where the pilot can not make suficient time to carefully and correctly run a well designed checklist.
Engine Failure at low level on a single or light twin
Fire
Running out of fuel
That is probably the only 3 occasions where there will not be time to execute the required actions and then run the checklist. Even the second two may give enough time.
I fear that your need to use memory rather than the written checklist stems from the problem that that chacklist contains far too many items.
I teach my students to only view the checklist when they're on the ground and parked. Ultimately you can't control an aeroplane safely if you have your head buried in paperwork!
Perhaps you might considder getting your student to learn the SOPs and the procedures / flows for each phase of flight and then have them complete a very short checklist at the appropriate moment.
After all, how many schools call BUMCPFHH (or similar) the pre-landing checks when in fact that are the pre-landing flow. The pre-landing checklist can simply be Mixtures Rich, Props Fine, Gear Down. Tell me that there is no time to read that and you have to be rushing unnecessarily.
Schools in general put very little thought into their SOPS, flows and checklists. They prefer to use a generic "checklist" which they sell to the students. The teaching of checklist use is practically non-existant. Exercise 1 and 2 is all but ignored.
Ultimately you can't control an aeroplane safely if you have your head buried in paperwork!
Makes me wonder how they read the map, record the progress on the OFP and brief the arrival procedure etc?