It's absolutely a workable idea. Standby instruments are typically a requirement for glass cockpit aircraft, and before electronic standby instruments came onto the scene mechanical instruments were used in the standby role in (AFAIK) all sectors of aviation.

"Fly the airplane" is the highest priority in any aviation emergency, and in many emergencies you will need backup instruments to do so. I don't mean to be mean, but tbh it is a little absurd to suggest that a e.g. a pilot who loses her PFD in IMC is better off running checklists than using backup instruments to establish control of the aircraft and situational awareness, and bailing out asap. Sure, it's stressful, but it's also something pilots need to (and do) train for.

Once the aircraft is under control, you can run your checklists, or if you have a co-pilot you may be able to work in parallel. Maybe you will be able to fix the issue, and maybe you won't, but backups give you a shot at landing safely either way.