[harimau777]

Even though we don't have long term experience the way we do with cooking, the description of the process on Wikipedia seems to suggest that it doesn't have much in the way of chemical effects on food. I'm definitely not an expert, and this is just an initial take, but I don't really see any mechanisms that could plausibly be dangerous.

In order to illustrate what I mean by a way that something could plausibly be dangerous: My understanding is that the molecules in most plastics contain chemicals that are known to be harmful. So even if we determine that it is not possible for them to break down into harmful chemicals in the body, it was plausible that they might.

Am I maybe missing some what that this process could be harmful?

[burfog]

The pressure may cause the container to release molecules into the food. Plastic that is normally considered food-safe might not be food-safe at these pressures.

[rbmktechik]

They explicitly state that they don't really know how it affects proteins, only that they are changed in "complex" ways.

Here is one example of a protein change which is deadly: https://en.wikipedia.org/wiki/Prion