I think the problem is one of simplicity vs complexity. New systems today rely on dozens - hundreds even - of packages and libraries - many of which are not written by the implementer. How can you ensure reliability in all these components?
This is why engineering from first principles - even in today's software development environment - is important. Unfortunately, the trends are in the other direction.
When the software fails (if it did) we assume the software makes it more dangerous because we have a concrete example of what happened but not what could have happened in it's absence.
This is what may eventually stall self driving cars for many years, the first time one does the PR equivalent of smashing through the local orphanage.
We as a society are notoriously poor at assessing systemic risks.
Now to address your point about evidence, I'm curious how you could control for other confounding factors.
Airliners are safer today than ever before (based on passenger miles) but how do you control for better engines, material science, procedures if you compare say 1979 to 2019.
But I have a friend who's an airline pilot. He was telling me about hitting windshear while coming in for a landing. The plane has software that not only tells him that he hit windshear, but also tells him what angle to put the nose at for best results. (The problem is airspeed. So you go to full power, but pitching the nose down also helps you gain airspeed. But the ground is down there, because you're coming in for landing. What angle is the best? The computer can figure it out and tell the pilot what to do.)
My suspicion is that modern computerised avionics are on balance a life saver but I'd love to know by how much.
I ended up watching videos of modern avionics in light aircraft on youtube a while back (as you do) and I find that kind of programming fascinating, couldn't find much out about the actual hardware/software side of things though I did gather it runs a custom OS.
This would be funny if it weren't tragically wrong. Time and again we learn that software is very much not yet well understood, especially in large and complex systems. And aviation does this a lot better than most other lines of business.
Sometimes software fails and sometimes it even kills people, but how many lives has it also saved because of things like collision avoidance and accurate navigation?
If you have several small distinct systems, you can often quantify them down to inputs, outputs, and expected logic. Once systems get too complex, you have too many possible states, and bugs are harder to find (and the system cannot be fully defined).
I often go back to the famous Therac-25 accident. The bug in Therac-25 existed LONG before the accident, but there were two systems interacting, one system checked the other system's output and threw away invalid state. Once those two systems were merged, it was only then that the bug turned into an accident.
If aircraft stopped building monolithic software and instead built parts that ran on software, parts that could each be individually verified, it would likely result in safer software.
When learning to fly sailplanes, I was always grateful that the "primitive" wood, steel and canvas gliders I flew had purely mechanical linkages between the controls and the control surfaces, and only one instrument that required electricity at all (and even that was duplicated by a purely mechanical version).
Obviously automation has great advantages, but inevitably the increased complexity comes with risks which are more difficult to fully comprehend.
I do not understand this point of view.
If you don't have software, you are going to replace it with something mechanical. Or with people. Or lose the functionality entirely.
Do you want to bring back a 'flight engineer' to operate airliner engines?
Do you want to bring back mechanical autopilots? Analog computers? Let's ditch GPS while we are at it (GPS failures can cause deaths, specially under poor visibility).
I believe this is what Airbus uses: http://www.esterel-technologies.com/products/scade-suite/
It does not mean that any software done with this tools is thus certified, you need to apply the safety methodology to certify it