I’ll have a crack at your assessment of overheads in a second.
Spinning reels I hold the rod in my dominant hand and wind with my left. I can cast more accurately, manipulate the lure, feel taps and react quicker with my dominant hand driving. I don’t have to switch after the cast and due to the lack of torque with a spinning reel I pump the rod with my dominant arm and then crank the line as I drop the rod toward the fish which requires the coordination and strength that my right provides.
Conventional’s from experience make more sense being right hand crank. Most overheads are trolled or we are soaking a live bait - usually from the rod holder. You’re not manipulating the rod. They’re also fishing heavy drag and capable of being used as a winch. I don’t pump and wind with an overhead, I winch the fish in. Often as I’m driving the boat towards it.
The right arm is doing almost all the work. I also have to manipulate the drag lever, the clicker, switch between low and high gear and due to the shorter cranking radius it takes more dexterity to crank an overhead then a spinning reel as you can’t engage your forearm. Being as I’m ALWAYS cranking against the drag to keep pressure on the fish it’s fatiguing and I can’t see doing it with my dumb arm.
A lot of fishermen also use a harness and don’t actually “hold” the rod. Strap the rod into a black magic belt and all your left is doing is using your thumb to lay the line down evenly. I don’t use a harness but my left arm just has to stay straight and hold on, very little technical work being done although the amount of drag takes its toll.
Baitcasters??? Someone else probably knows. If I had to guess it’s rooted in bass fishing and they probably know why they’re doing it. If I had to guess it’s because they can make those little tiny circles faster with their dominant hand and that’s more of an advantage then what switching hands during or after the cast is.
This is what I consider normal for both types.
Slow pitch jigging reels are right hand wind as well for a plethora of reasons.
As always, most of us do what we were shown by our fathers or whoever taught us to fish. I think there are technical reasons for doing it certain ways but it can be done however you want. As long as you’re not holding the reel upside down, who cares.