I started out in the hobby reading Julian Sprung's work, Albert Thiel, Shimek, Bob Fenner, Dana Riddle etc etc. I've seen the hobby kinda evolve from different methods and new technology. I get that. And I personally think each of those guys probably did the best they could with the info they had at the time.
For sure, many of us though, always though the hypotheses to explain how a DSB and live-rock worked, were lacking. Shimek for example, came up with ideas about worms and other critters, moving through the pores of a rock, would transfer nitrite into the pores where the denitrifying bacteria live. This always seemed like a clunky explanation. We now know though, that bacteria grows in films, that create a micro-environment, where bacteria and other organisms share products amongst the community and modulate the permeability of various chemicals and molecules etc.. The bacteria which use nitrate, and converts it to N2 gas, do so, only if O2 is low. As it turns out, these bio-films though, are not actually very permeable to oxygen. As described here
Biofilm Gradients.
So, O2 actually can become low enough for denitrification to happen within micrometers of any surface, due to the low permeability of bacteria in films, which form on surfaces within minutes in saltwater. The bacteria at the bottom then, would be expected to use nitrate, rather than O2, as O2 is no longer available. So, the old myth that you need lots of sand to decrease permeability of O2, just doesn't seem to hold true based on what we know today. The reality is you just need films to form on the surfaces. More sand may help, as it may increase surface area, but it is the film decreasing permeability as well, not just the sand and the film should do so more reliably I think, as the films will not tend to get overly thick.
The issue with sifting would be that after N is low, then the bacteria will start to use sulfur and produce hydrogen-sulfide. With a shallower sand bed, you'll have less risk of that and can stir away and honestly, I have never had issues with nitrate with shallow sand beds. I think, there is a lot of surface area in a shallow bed. Going beyond what is necessary, likely just increases the odds of the sandbed becoming a nutrient sink, which, is probably why people turned to bare-bottom tanks to get lower nutrient systems. Really though, I think a little sand can help and look good, it's more overdoing it, do the the incorrect belief that it is the sand that reduces O2 permeability, that is the problem.