One of the big challenges here is that these recommendations may change over time as people learn more, discover different trade-offs that need to be balanced, etc. For example, Kunze actually changes his own suggestions if you read through different editions. For example, in the 3rd Edition (2004) he directly notes that "It is therefore of interest to considerably reduce the pH to 5.1 to 5.2". While he mentions that this can be done either during the mash or in the kettle, in this edition he clearly states many of the noted benefits other have mentioned here when directly speaking about mash acidification, and also notes that Alpha-amylase is slightly inhibited by doing so, which further suggests that he's explicitly recommending 5.1-5.2 in the mash.
In the 6th Edition(2019), he unequivocally states that "it is therefore advantageous to lower the pH value to 5.4 - 5.5 when mashing. The Beta-amaylase can be damaged at lower values". Note that I'm 99% sure that the reference to Beta here is a typo/translation error, as there are actually a number of them throughout the book, earlier editions clearly reference alpha (not beta) being inhibited at lower pH values, and numerous other sources note alpha having a higher preferred pH range. Anyway, he then goes on to discuss a number of similar benefits of wort pH in the 5.1-5.2 range, but is fairly unclear about "when" during that discussion, which is interesting. The mash pH, recommendation, though, is direct/clear.
Anecdotally, in the handful of mashes I've started recently tracking pH through, I've noticed that those I targeted/initially hit 5.2 and those I targeted/initially hit 5.4 both seemed to stabilize around 5.4 over time. These have all been step mash schedules >60 minutes (Hochkurz or "Brauwelt"), FWIW, and salts/acid were used initially to target those lower pH values.
Here's something from Kunze (3rd. Ed) that might be relevant. As noted, he discusses targeting pH 5.1-5.2 directly in the mash, but then discusses wort/kettle acidification in addition, stating that "These are all good reasons for a biological acidification at the beginning of mashing. Since the phosphatases release a considerable portion of the phosphates, which which play a substantial role in the buffering, the pH shift is partially compensated. It is also therefore worth acidifying the wort. We will see, however, that the wort acidification should preferably occur at the end of or after wort boiling." He then subsequently restates the optimal pH of 5.1-5.2 as the target during wort production, which seems to suggest that one may need to "re-acidify", presumably because the mash pH will creep up a bit. I'll freely admit that I don't understand the chemistry well enough to state that is the case absolutely, but it's some food for thought.