Maybe just to go back to basics for a moment
It's prety much a truism that pH should fall at every step in the process and mostly by the same mechanism. Namingly the reaction between Calcium and Phosphates in the malt forming insoluble Calcium Phosphate. The obvious limitations being the availably of Ca and Phosphates. Given enough Ca as part of your salt additions to mash and sparge water (50-100ppm at a minimum). The limit becomes Phosphate availability, not all the Phosphate is available initially, some of it is bound up in organic complexes that are liberated during the mash and boil, so we should see a steady fall in pH as Phosphate becomes available.
For this reason in a pale beer mash (bit different for dark beers as Melanodins are acidic), no matter how much Ca we add as salts the initial mash pH in distilled water will rarely get under 5.6pH, somewhat above the ideal for mash enzymes. Adding acid to reach the optimum pH is again pretty common practice.
Using acid to adjust end of boil pH to the optimum for the yeast and adding some of your Calcium at the end of the boil are both pretty common to (well in really big breweries).
So yes I'm pretty much going to agree with you having the pH on target at every step will improve your beer.
Baring the unexpected, if your mash pH is on the money and your water chemistry is good (lots of Ca say >150ppm) and you dont have too much residual Carbonate, your pH should stay on track, you should also have plenty left over for the ferment where it benifits yeast and helps with flocking and sedimentation of both yeast and some of the other break material.
If you want kettle finings (Carrageenan) to work well, the pH is critical there to, being not far from target can have very negative effects on how well kettle finings work...
It's also well worth testing end of ferment pH to. Small adjustments can make a big difference there. Beer over the range of 4.0-4.5pH can go from being described as Too Sharp - Brilliant - Flabby (the average for Lager/Pilsner styles is around 4.1-4.2pH). Well worth doing some tests in a glass you just need some Lactic acid, a bit of Bicarbonate (make a solution) and a good pH meter.
Look forward to seeing how you go, please keep us informed, this is an important and often much ignored part of brewing.
Mark