Why does the 'Positive-inside Rule' exist?
There are not much explanations available, as far as I can see. The best explanation that I have found is that the positive charge allows the orientation of the protein in the membrane. The orientation for membrane proteins is important as a lot of them are transporters which have a dedicated transportation direction. The same is true for receptors, which transport a signal from the outside to the inside of the cell. Most of the positively charged arginine and lysine residues are found in loop regions which are located between transmembrane regions (often hydrophobic helices).

References:


Topogenic signals in integral membrane proteins.
Positive charge loading at protein termini is due to membrane protein
topology, not a translational ramp
The Positive Inside Rule Is Stronger When Followed by a Transmembrane
Helix
Membrane-protein topology