Interesting points, especially about the challenge of correlation. I guess we could remove DNA and see what happens ...
Somehow the machinary is passed down: Do we know of another mechanism besides DNA that is self-perpetuating? Is there any living creature without it? Prokaryotes (bacteria) even have DNA.
Or is there a way to do it without self-perpetuating mechanisms? Is that logically possible? Some machinary might be perpetuated by other machinary, e.g. the chemical might recreate the electrical, meaning it's not self-perpetuating. But that's not different than DNA: DNA itself isn't the machinary, but its self-perpetuation is what recreates other parts.
I suppose some parts of the environment are consistent, such as sunlight, air, water, and heat, but the environmental stimuli must trigger something that is already there.
> I guess we could remove DNA and see what happens ...
If I have a stool with three legs, and remove one leg causing it to fall, can I conclude that removed leg is what made it stand?
You’re making the same mistake as before in reverse: DNA would do nothing without a host cell or chemical signals, either.
> Somehow the machinary is passed down: Do we know of another mechanism besides DNA that is self-perpetuating?
The system as a whole is self-perpetuating, but DNA is not self-perpetuating: without a host cell and without ambient chemical signals, it cannot propagate. That’s in contrast to ribozymes which can be self-catalyzing RNA, ie, truly self-propagating chemicals.
In the RNA world hypothesis, such self-catalyzation was the origin of life; and by the time DNA evolved, it did so within a running biological system and as merely one component of cellular replication.
As a whole the system of chemical signals, DNA, and cellular machinery propagates; but just like our stool example, removing any of the factors causes that to fail.