Let me bore you explain: I’m discussing complementary, interrelated approaches and considering their relative merits.
Covering the brakes allows you to react marginally quicker to tricky situations. Looking ahead and reading the traffic in order to identify and tackle potential and developing hazards ("anticipation" if you prefer) extends the window considerably further. They are connected factors in that they both affect reaction time. We appear to agree that the latter factor is likely to be of greater importance in avoiding a collision (and can offset the former and allow you to not cover the brakes 100% of the time?), but hazard perception is a skill that comes with experience/practice; covering the brakes is not a skill in itself, but understanding braking distance and your braking limit is. Where it appears we diverge, is that I’ve always found it more constructive to think holistically about cycling safety - that’s not to say one shouldn’t prioritise, or even think in terms of black and white on occasion, but reducing this issue to a simple dichotomy does not take into account and assess the context, similarity, difference, importance, and interdependence of various approaches in a dynamic traffic situation.