The point you bring up about different areas having different multipliers is well worth pointing out. Among other things, an income multiplier is a (rough) measure of a number of factors in an investment. One of those factors is the risk involved with the property type, location, condition, etc. Another factor is the amount of competition at those prices in the sales market and the rental market, which don’t always move at the same pace or even in the same direction.
So yeah, you would expect GRM/GIM indicators (which are factors) to be higher in the more desirable locations and lower in the less desirable locations. You would expect them to be higher for the newer and better condition properties and a bit lower in the inferior condition properties because of maintenance and replacement costs as well as the lower rents. Bigger risks require bigger returns, which in turn reduce the rent multipliers.
Finally, it bears repeating (again) that rents are tied to local wages, not investment income; there are definite limits to how much people will spend on rents. People who retire from Phoenix don’t bring their nest egg to rent; they buy. Percentage-wise, the difference in rents between otherwise similar 2bd/2ba homes in La Jolla (93137) vs. Barrio Logan (92113) is nowhere near the difference in sale prices.