I've taken some ceiling tiles down in prep for running network cables through the house and found some questionable electrical work. As I understand it these wires probably wouldn't be okay even if the ceiling was completely open because they're 12 AWG and running perpendicular to the joists, but I want to confirm whether or not these are supposed to be run through holes in the joists.
This is a simple one when exposed smaller gauge requires a backing board to be run perpendicular to the joists. There is a pretty picture exhibit 334.1 this is for crawl spaces and basements code gives no height restrictions but local code may.
This example where it was covered was a code violation the cable required a nail plate at each joist in this example because it is less than 1-1/4” from the face of the joist (so you are correct it was a bad thing to cover)
The best way to fix something like this is to pull the cable out drill a 3/8 hole so the edge of the hole is at least 1-1/4 inch back from the face of the joint and pull the cable through the bored holes. That could bring it up to code.