On the shortcomings of the Shapiro delay tests of the equivalence principle

There are several shortcomings in the "standard" Shapiro delay tests of the equivalence principle on cosmological scales \cite{minazzoli:2019pr}. Although many people in the community already acknowledged this in the literature, and proposed alternative ways to compare potential Shapiro delays over cosmological scales -- e.g. \cite{bartlett:2021pr,hashimoto:2021pr} and references therein -- papers are still submitted to journals with the usual issues.