What is the mechanical world picture?

> it is only natural that the mechanical world picture would initially think of natural phenomena as operating according to externally imposed influences (motion imparted from outside, laws of nature, or what have you) rather than something intrinsic to them.

Laws of nature are not externally imposed influences. They are human descriptions of what we observe to happen under certain conditions. They are called laws because we have no reason to think they are ever violated.

Doubling your distance from a point source will quarter the energy you receive from it. Not because of any externally imposed influence but because an intrinsic property of a sphere is that surface area increases according to the square of the radius.

> as the mechanistic conception of the world developed, it essentially came to be about eschewing anything that smacked of final causality

Scientists would love to know if there is final causality other than the universe itself. However, evidence is the only way to separate reality from make-believe and there is not one scintilla of evidence that anything exists apart from the universe we see all around us.