Lying down when exercising is a bad idea, so why do so many people do it? We don't operate lying down; we sleep. Working a muscle, or muscles, when prone or supine or on all fours does nothing to prepare them for the reality faced 99% of our waking moments, when we are upright.
Our bodies need vertical stability, not horizontal stability. Gravity is the main factor to consider when performing an exercise, and when we are in a lying down position gravity has a completely different effect on us then when we are standing. As a hypothetical, take a bookcase that is meant to hold books in a horizontal position, and then tip it on its edge and watch all the books fall out. The books don't stay in the case because its being used in a manner not consistent with how it was built.
So if you get better at doing a plank or crunches (yuk!) or a TRX exercise, you are only better at that specific exercise while in the horizontal position. There is little, if any, transfer of strength to movements performed while horizontal.
The goal is horizontal stability, not vertical. So if you spend a lot of time exercising while lying down – bench press, crunches, planks, “hydrants” (yuk, again) – you are wasting your time.