I did not follow your other thread, so I don't know what it devolved into. It doesn't matter to me. It sounds like you and I are in the same camp, CAD is a prominent and essential part of my design/creative process. Since I have been a metal machinist for decades, it has come out of that. I create CAD drawings for nearly everything I do, particularly in metal, but now also in woodworking. As with you, it allows me to think through things, both in design aspects, but also in practical ways. Over the years, I have found that if I make parts to the drawings, things fit together and most often, they work as intended. And if they don't, it is usually pretty easy to figure out why and correct for it.
I build my projects with each part on a separate layer, with another separate layer for dimensions. I build it will all the parts "in assembly", as they fit together. This allows me to design them to fit and allows me to think through how they would be made. Another aspect is when I am making something to add to an existing tool or device or equally or more often when I want to modify or repair an existing item. I measure and draw the existing part(s) first and then start adding or changing things as needed, still using the separate layers method. I can print in assemblies/sub assemblies and then each item in turn, as they might be assembled in sequence. I've used this latter technique for explaining things to someone remotely. Usually, they can see and understand what is happening or what I mean to do. This is most often the case when I am making/modifying/fixing something for that someone else.
I have been using an old AutoCAD product, AutoSketch, which isn't supported anymore, but it still works fine. I have had versions of TurboCAD 2D/3D on my computer for years, but the learning curve has been more than I have been willing to endure. Last year, when I was making wooden gears, I learned enough 3D CAD in Fusion 360 to produce drawings that were sent to a CNC router guy. Unfortunately, I haven't touched it since, so I'd have to climb most of that hill again. It would be nice to be able to work in 3D, as most other folks seem to relate to it better than 2D drawings.
I really enjoy the process, in which CAD is an integral part. And when the project is done, I turn the pages over and use them as scratch pad paper at my computer station.
"Quality is like buying oats. If you want nice, clean, fresh oats, you must pay a fair price. However, if you can be satisfied with oats that have already been through the horse, that comes a bit cheaper."