So why did the Fed valuation model become a zombie? - The Fed killed it.
The model is based on the assumption that there should be a relationship between the earnings yield and interest rates for long-term bonds. Both discount future cash flows. Investors should be indifferent between between these yields. If the earnings yield, (inverse of P/E), is high (low) relative to bonds, investors should buy (sell) stocks and sell (buy) bonds. Of course, this is a relative model which tells use the richness and cheapness of both bonds and stocks. If one is rich, the other is cheap. It suggests that one may do better or worse than the other and not whether one market will have an absolute gain or loss. Unfortunately the Fed model has failed for some time.
There is no doubt that inflation has been low for most of this period. Additionally, there has been a downward trend in real rates of interest based on a number of solid reasons which can be a cause for the divergence. Of course, determining the equilibrium rate of interest is even more difficult when rates are close to the zero bound. But, a key reason may be the manipulation of interest rates by the Fed. A manipulated rate should not be used as an anchor for relative value. Following the Fed model would have been financially dangerous.