I think it probably can serve as a somewhat useful heuristic at extremes. I am pretty sure this isn't the case here and now, so it would be very difficult to draw any specific conclusions.
Not my research, Research done by AQR and other paper by Estrada. Where is your research or quote to support your position? BTW, if you look at first chart posted in the this thread, what ever empirical fit has worsened since 15 years. You don't need another research when the fundamental position is flawed. It was just a empirical fit for certain period that too just in US. That logic falls apart in other countries and in different period. 2007 paper by Estrada "The Fed model: The bad, the worse, and the ugly" http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.586.1041&rep=rep1&type=pdf
It's actually a fascinating and rich subject... You can read some more recent stuff, where the conclusion is that for all these relative comparisons, all the higher moments of the asset return distributions really matter a lot.
2012 study by Vanguard: "Also of interest is the result for the Fed Model, which we find has had poor success in predicting long-term stock returns; its R² with 10-year-ahead returns is 0.16. This is less effective than using the earnings yield by itself"
"Empirical fit" of almost any model is worse out-of-sample than in-sample. In other news, water is wet.
This speech by a BoE guy talks about these things in a way that I found more understandable than the academic stuff (pages 3 - 12): https://www.bankofengland.co.uk/speech/2017/real-interest-rates-and-risk There's a bibliography in there with references to papers.