Depopulating these type boards increases the value of the board itself and reduces the shipping cost. I refer these type board as power/logic boards and have found many in laboratory and medical equipment. I would also remove the battery, capacitors and heat sink. I remove the transformers using a wood chisel.
I am assuming you have determined that there is no resale value to these boards. I don't know your experience level so I will just tell you what I would do with the boards in the first photo.