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.