" . . . a similar line of reasoning notes that animal burrows and plant roots, etc., can be found on every modern soil surface, on land or in water. Why are they rare to non-existent in the geologic record?"
1. The immense pressure crushes such things, especially anything resembling a void. They may or may not be there --- we have no idea (you'd just have a crack, at best).
2. While certainly not commonly found, who says they are rare? The chances of coming into contact with one with a core sample (and recogonizing it for what it is) is slim and none. A bit would just give you dust --- lucky if you get micro fossils.
3. Drilling activities generally occur in former sea/reef beds because that is where the oil/gas. No trees or gophers at the bottom of the sea.
This is just the before coffee answers. I could go on.
Investigate "sand frac jobs" to learn more about the immense pressures involved ---
---- I will not be responding, as it is like pounding a drill bit against a closed rotary table having these discussions.