Even after years of research, why are planes unable to keep passengers alive in case of a fiery crash?
Short answer

The kinetic energy involved in a plane crash is inhumanely high.

Slightly longer answer

We can built bombs which will go through concrete roofs and ceilings of a bunker, counting the number of floors they crash through while descending so they can explode at the level where the bad guys sit and not where the widows and orphans are kept. We could equally well build a plane with this kind of strength, so the fuselage stays intact even when it crashes into a mountainside. That's not the problem.

Limits of the human body

The problem will be that rescuers will only find dead bodies inside. The human body was "designed" to endure things like running into a tree, but not being hurled around at Mach 0.85 and then being stopped almost instantly. Thanks to years of research we now have quite a good idea where the limits are. Martin Eiband collected a lot of data on this, if you want to know more, google for "Eiband diagrams". If you want the full picture, read the Army Aircraft Crash Survival Guide. It comes in five volumes, and volume 1 covers the design criteria. The Eiband diagram below is lifted from this source.


Note the time scale: A deceleration with 40 g can only be tolerated for a duration of 0.1 seconds; if the deceleration takes more than 1 second, the limit is only 10 g. Now let's see what deceleration distance is required to stop a human with an average deceleration of 10 g. The energy $E$ of a body of the mass $m$ increases with the square of speed $v$:
$$E = m\cdot\frac{v^2}{2} = m\cdot a\cdot s$$
At $a = 98.0665$ m/s², the stopping distance $s$ from an initial speed $v$ is $\frac{v^2}{2\cdot a}$:


Car crash at 30&nbsp;m/s: This needs 4.6&nbsp;m and good restraints, but is generally survivable.
Free fall at 60&nbsp;m/s terminal velocity: 18.4&nbsp;m. A few humans have indeed survived this by falling into soft ground like a snow-covered conifer forest. This is also the typical approach speed of airliners, and the 18.4&nbsp;m is the fuselage ahead of you. That is the reason why a crash is more survivable for the occupants in the rear seat rows.
Propeller airplane flies into mountain (120&nbsp;m/s): 73.42&nbsp;m. This kind of crumple zone is simply not available, and nobody has survived such an impact.
Airliner flies into a mountain (240&nbsp;m/s): 293.7&nbsp;m. To make such a crash survivable, every airliner would need to carry a 300 m boom of stiff material around which would be needed as a crumple zone in an accident. Just think what kind of aft fuselage and tail this would require.
And to top it: Astronaut on a space walk collides with a satellite in an opposing orbit (16,000&nbsp;m/s): 1305.23&nbsp;km. Note that I had to switch units to keep the number manageable.


Please consider lower deceleration limits for elderly and untrained persons; the limit in the Eiband diagram was established using healthy young pilots (and hogs, chimps and corpses for the higher limits. A lot of blood was spilled to arrive at these numbers).

The problem is not the aircraft structure, it is the fact that humans like to go fast but are not built to stop quickly.