>So, should all trials be run with one strata? That is the logical outcome of your contention.<
That’s not a reasonable thing to do in practice; however, sponsors should strive to run relatively clean trials where Cox is relatively inconsequential. A trial such as the one you posited in your example (which was extreme for illustration purposes) would be ridiculous to run if the effect of the psychological profile were known a priori.
Cox does not obviate the need to run well-designed trials.