I cast my vote in favor of implementing checklistsin the EFIS but with one provisal: they need to be implemented in a smart way which takes advantage of the fact that it is running on a computer which knows a lot about where I am and what I am currently doing.
There are checklists for various phases of a flight: engine start, taxi, take-off, climb, cruise, descent, arrival, landing, shut-down and emergencies (to name just the more common ones). The EFIS should know which checklist I want and present the most likely choice in a convenient manner to me. Emergency checklists should always be available with the least amount of menu browsing.
The checklist should automatically fill those items which it knows about (i.e., air speed, engine rpm, electrical voltage, etc, etc.). The pilot should still be required to acknowledge the value but it would be convenient to see it right there on the checklist. So, e.g., the item "Engine rpm set to 1000" would turn "green" as soon as engine rpm is 1000 rpm (give or take a little). So there ought to be 3 states an item can be in: unchecked, value checked by EFIS, item confirmed by pilot.
The EFIS should issue a warning that there are unchecked items on the list at predetermined phases of the flight. If you start the engine prior to working through the startup checklist, the EFIS would complain. Similarly if you start to taxi before the pre-taxi checklist, etc. Getting close to your destination should prompt you for the arrival check. And within, a pre-determined distance and altitude from your landing spot you should be prodded to work through the landing checklist.
I know this is not a trivial addition to the functionality of the EFIS. But it would be the only justification for having checklists on it. A simple sheet of laminated paper is still better if all you want to achieve is displaying static and unchanging information.
And, by the way, there ought to be a simple way of shutting the EFIS up when it complains about checklists not having been worked through.
Greetings, -- Chris.