I would argue that there isn’t anything inherently “wrong” about a standard electric guitar design, although certain body styles do influence certain habits. I’ve discovered that when I’m doing scalar picking I’m a wrist deviator ala Eric Johnson, so playing my rhythm guitarists’ Xiphos was awkward as hell since there isn’t a nice place to support the forearm, you pretty much have to be a rotational picker on pointy guitars.
That being said, I can’t see making an electric guitar “fatter” making things any more or less easier to play.
There is a physical reason that the “lean” makes things easier to reach… you are spreading apart the shoulder blades and getting more of the upper torso and arm around the perimeter of the guitar. I see this in young guitar students who most likely have really strict parents always yelling at them to sit up straight. Their shoulder blade movement is severely restricted and they have trouble reaching around the neck of the guitar.
Theoretically, a fatter, more acoustic guitar design could force a player to do this, but I suspect if a guitarist isn’t inclined to naturally go to this movement that they would probably feel even more restriction on a fatter body than on a slimmer one.
Also, with @GTR continually referencing Joey Tafolla… perhaps he does the movements you are describing, and I’m sure he’s a fantastic player, but for one player’s example I can find ten or twenty that do something different and are highly skilled and effortless musicians. I would suggest a smarter thing to do would be to find a consistency that all or most players do and find out what that is and use that as what you’re looking for. And I can assure you, most all players will do some form of the “lean” to get those shoulder blades moving at some point or another, and depending on their body size it can be more subtle, or more pronounced (like in Gilbert’s case).