Additionally, this might make pilots more reluctant to declare an emergency, which would have a negative impact on safety.

Indeed! It's mind-blowing the number of conversations I've had online and in-person where pilots say something like "I didn't want to declare an emergency, because I didn't want to do a lot of paperwork." Invariably, someone (sometimes me) asks "for those of us who have declared an emergency, how much paperwork was involved?"

In ~95% of declared emergencies, there is zero paperwork or followup required. In over half of them, the pilot elected to (voluntarily but advisedly) fill out a NASA ASRS form (which is about a 15 minute task and something they probably would have done under the same circumstances without the emergency declaration). ( https://asrs.arc.nasa.gov/docs/ASRS_ProgramBriefing.pdf )

This might well be somewhere that you can improve with training. It reminds me of the situation for CAPS (the Cirrus Airframe Parachute System, a ballistic parachute for Cirrus small planes). Once you train pilots to specifically plan to use CAPS when things go wrong, rather than relying on them realising in time after something has gone wrong but before fatal injury is inevitable that the CAPS can save them, you get significant improvements in save rates.

It may be that training pilots specifically to declare emergency as soon as there's a problem rather than waiting until they're sure they can't solve the problem and need outside assistance will improve overall safety outcomes.

There's a tragic case I watched a safety video about where the private pilot, very low on fuel, asks if he can land at a (closed) airbase whose traffic controller he's talking to. The base's controller says he cannot land unless he's an emergency. That was his last chance to survive, all he needs to do is say he's an emergency - "I'm on fumes, I need to land right now" she'd turn the base's lights on, he puts it down on a strip that's not meant for civilians and maybe he spends the evening explaining to some MPs how he fucked up - but he's not dead. Instead he accepts this as a "No" and flies on for a few more miles until he runs out of fuel and crashes.

Indeed the improvements in Cirrus training and communications has had a fleet-wide positive effect. I do think calling all of the no-life-lost deployments "saves" is disingenuous at best and more likely intentional shading of the truth. We don't call every airbag deployment without loss of life a "save" but we can draw database-wide conclusions about how many net lives were saved. In CAPS case, I don't believe the most accurate estimate of lives saved (vs a counterfactual where the airplanes did not have CAPS) is 258 across 126 events, as many of those occupants would have also survived the event without CAPS.

PS1: I saw what I think is that same ASF video ( https://youtu.be/fLlWf-Fk_YM?t=10m ). Really frustrating, especially how obvious it was an emergency to everyone except the two people on the radio (where the bulk of blame belongs to the pilot of N4975S.

PS2: One of my instructors was in CAPS Event #59. I talked to her afterwards; she was a fan. :)

I think the airbag comparison is a bit off, airbag deployment is automatic, so it may be that all the humans involved were like "This is fine" but you tripped the impact limits and so now there's an airbag deployment, CAPS isn't like that, a human has made the conscious decision to deploy.

Yes, but the outcome is still a statistical improvement over a non-zero baseline. Some of the stricken Cirrus would have been landed with zero fatalities (likely including my flight instructor's case).

Calling them all "saves" is overstating the incremental benefit.

The paperwork is often NOT government mandated; there may be corporate mandates, too around it.

(I've technically declared pan-pan once, there was no paperwork.)