We have two different things under consideration here; 1) the depth of the lure, and 2) the action of the lure.
The depth is affected mainly by the diameter of the line and in a minor way by the hydrophilic/hydrophobic quality of the surface finish. The more resistance the line has, the more it "pills up" the lure. The less resistance it has, the more the lure is allowed to fall. Roughly speaking, you're correct about line diameter; lines of the same diameter affect the lure the same.
There are two kinds of action; native and non-native.
Native action is the action the lure would have if it were entirely free of drag and damping effects; in other words if it were in a perfect environment. For most cranks, this is a side-to-side wiggle, rock or vibration. For spoons, it's usually a wobble.
ALL OF THIS CAN BE OVERCOME. Many fishermen tie directly to a crankbait, believing that it's the best way. Sometimes it may be, but sometimes it's not. If the knot is not a loop knot, but tied directly to the tie eye on the lure and pulled tight, and the line is "stiff", the action of the lure can be noticeably impaired. There's nothing wrong with tying directly to a lure, just make sure the lure has an easy range of motion. Some use a loop knot, like a Rapala knot or surgeon's loop, and other use a snap. If you want to know the difference for the lures you use, the solution is easy; get some snaps and try your lures both ways, watching the results carefully.
Now ..... a little force can be good. It either enhances the native action of a lure, like pulsing a spinnerbait or twitching a spoon, or it gives action to a lure that has none of its own, like walking a topwater or hopping a tube. That's good, not bad. But it needs to be selective and controlled.
So what the fisherman actually does during the retrieve has a lot to do with it. You either cooperate with or fight the action of the lure with your choice of knots, speed and line.
Also; if a fisherman retrieves at too high a speed, he defeats the native action of the lure. A fast retrieve can even defeat the design of a diving lip, resulting in a lure that runs far too shallow or that spirals out of control. That's not good. Thankfully, it's also not common. You need a lure that lacks inherent stability for it to happen, and I throw those lures away.
Usually, fishermen retrieve lures too fast, although I admit not extremely fast. But slowing down can change the way the lure works .... and get you more fish. Common sense is the rule of the day.
Now .... the bad news.
All this is the stuff of fine-tuning. It's not stuff that hits you over the head, jumps out of the water or changes lures from what they are to what they're not. You said that it's an analytical person's nightmare, didn't you? It's not .... it's an OVER-analytical person's nightmare. All of these things can be noticed or discovered by the average fisherman under average circumstances, if they just watch carefully. No need to go gonzo.
Always remember: You control what you do, what you do doesn't control you.
Hope you have more fun fishing, because in the end, fun is what it's all about. ? jj