Parachutes are a lot fiddlier and less reliable than the layperson assumes, so the baseline for how complex a system like this can be is worse than you'd think.
"I've never found myself packing a backup parachute, because if one parachute can fail, so can its backup one. And now you've got two things to worry about."
The envelope that ballistic parachutes provide a life-saving emergency resolution vs a well executed power-off glide is pretty narrow. The studies show that far too often it is abused by providing a false sense of security, encouraging pilots to take risks they otherwise wouldn't have.
It’s worth noting that it’s not the parachutes that typically fail, rather, the deployment systems.
You’re packing (by hand) a large area of fabric and cord into a very small volume. You’re coating that fabric and cord with a variety of anti-stick substances, which have to be stable with extreme temperature and radiation levels, and huge vibrations.
Parachutes are deployed in several ways - springs, hydraulics, compressed gas, explosives, drogues, and combinations thereof.
For flight tests, parachutes are typically pre-stressed as though they’ve been to orbit and back. This wasn’t always the case.
So - there’s a lot of surface area to go wrong purely around the problem of getting it to eject and unfurl, before you even start to think about the parachute itself.
While a parachute is helpful in certain situations it's better not to fall out of the sky to begin with. It is, so to say, a poor workaround for the real problem.
If you look at how a parachute is packed, and how it unfolds when deployed, what you described is definitely not the simpler explanation preferred by Occam's razor.
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