You’ve deeply misunderstood the reality. Whether that’s because those vids suck or you’re not following the explanation I can’t say.
First off, one engine’s generator can power 100% of the normal electrics, perhaps less some galleys and some inflight entertainment. So unless both engines or both generators have failed, you’re not relying on the battery for anything. If both engines have failed, you’re going to be landing soon. If just one engine or engine-driven generator generator is lost, the cockpit looks and works exactly like normal.
If both engine generators are out, the auxiliary power unit (APU) we use for electricity at the gate can be started and provide electricity for the whole airplane. Just like it does at the gate every day. The cockpit and all supporting system would be fully powered. Depending on the specific model of airplane, the APU may not be available at very high altitude. Generally older near-obsolete airliners have more weaknesses in this regard.
If all 3 of those are out, all airliners have a battery system that is guaranteed to provide 30 minutes of battery power to an adequate set of instruments. The 30 minutes is for an almost worn-out battery in a state of discharge. Most batteries will last longer than that; more like 60-90 minutes, maybe even 2 hours if the battery is near-new and fully charged when the AC power dies.
The 30 minute standard is enough to fly a couple hundred miles and descend from altitude to a normal landing before it gets dark. For folks over civilized countries that’s almost certainly plenty.
In the case of a modern jet that does somehow find itself down to the battery, essentially the copilot’s instruments quit as does some of the backstage redundancy. For example, 1 GPS receiver stays powered, not the usual 2 or 3. So the Captain’s looking at all his usual stuff and the FO is looking over his/her shoulder.
Finally, there’s a last ditch separately internally powered standby horizon, airspeed, and altimeter that’ll run for another 10-20 minutes after everything else dies. These are small auxiliary instruments and it’s difficult to fly well using just them. But it’ll get the job done in all but the most adverse situation. But by the time they’re all you’ve got, you’re already out in the 1:several billion odds.
@Friedo points out RATs. Airliners that are certified for long haul overwater may not be able to reach an airport in the typical 30 minutes allowed for by just the battery. So there needs to be a way to stretch the battery. Enter the RAT which will provide enough power to avoid using any battery as long as you’re at a speed above landing speed.
Other solutions to the extended flight without engine/APU generators problem are generators turned by hydraulic power. If the engines are running the hydraulics are pressurized. And like the RAT, a hydraulically driven generator will provide power as long as the engines run.
As a reminder, when all the engines quit the game is over once you’ve glided down to the land/sea. Which will take significantly less time than the 30 minutes the battery supplies.
So in priority order we have:
- One generator per engine (787s have 2 per engine).
- One generator per APU (787s have 2) .
- For long haul airplanes, 1 RAT or a hydraulically driven generator or both.
- One 30+ minute battery.
- One standby flight instrument package with another 10-20 minutes run time.
Running out of power for instruments is simply not a problem.
Obviously you can always posit enough cascading failures to overwhelm all this stuff. What if lightning strikes and melts every wire? What if a fire starts in the cockpit behind the main instrument panel? But that’s not the way to bet.
I’d be curious to hear of an accident that came from truly running out of electrons.