A lot of bad assumptions on your side imho.
1) Your daylight spectrum will have less photons/J than HPS spectrum, that's a fact.
=> If you had an imaginary HID, with equal efficiency to HPS, but with your daylight spectrum , it would produce less photons. It would also produce more leaf to bud matter, overall bud production per watt will be considerably lower.
2) Plants were originally algue (for most of their photosynthetic evolution and history). Algue did not receive and evolve with the same spectrum as plans are getting today, as the ocean acts a bit like a (inverse) phosphore itself. Algue adapted to better trap the red photons
3) The photon loss is much lower than you think. When going thru a phosphore, it's not so much a loss of photon as a loss of energy of those photons.
Take away enough energy, or slow down a blue photon enough, it will become a red one. It will have lost energy, but it's still a fill photon.
"Photosynthesis is the ability of plants to absorb the energy of light, and convert it into energy for the plant. To do this, plants have pigment molecules which absorb the energy of light very well. The pigment responsible for most light-harvesting by plants is chlorophyll, a green pigment. The green color indicates that it is absorbing all the non-green light-- the blues (~425-450 nm), the reds and yellows (600-700 nm). Red and yellow light is longer wavelength, lower energy light, while the blue light is higher energy. In between the two is green light (~500-550 nm). It seems strange that plants would harvest the lower energy red light instead of the higher energy green light, unless you consider that, like all life, plants first evolved in the ocean. Sea water quickly absorbs the high-energy blue and green light, so that only the lower energy, longer wavelength red light can penetrate into the ocean. Since early plants and still most plant-life today, lived in the ocean, optimizing their pigments to absorb the reds and yellows that were present in ocean water was most effective. While the ability to capture the highest energy blue light was retained, the inability to harvest green light appears to be a consequence of the need to be able to absorb the lower energy of red light.
Plants also use multiple variants of chlorophyll, as well as accessory pigments such as carotenoids (which give carrots their orange color) to tune themselves to absorbing different wavelengths of light. That makes it impossible to assign a single wavelength of best absorption for all plants. All plants, however, has chlorophyll a, which absorbs most strongly at ~450 nm, or a bright blue color. This wavelength is strong in natural sunlight, and somewhat present in incandescent lights, but is very weak in traditional fluorescent lights. Special plant lights increase the amount of light of this wavelength that they produce. But a 400-500 nm wavelength bulb wouldn't be enough, since many plants take cues for germination, flowering, and growth from the presence of red light as well. Good plant lights produce red light as well, giving plants all the wavelengths of light they need for proper growth."
So again a very flatish relative spectrum curve is NOT ideal.
3K/3.5K/4K + according amount of violet/UV + deep red is as close as we can get today to an ideal spectrum efficiencywise, and is probably superior to your static imaginary "daylight spectrum".
You are obviously over simplifying everything, a higher value of every nm on a relative spectrum curve does not mean there is more photons, learn how to read relative spectrum graphs.
Kind of like the thermal gradient in the atmosphere; a paradox of activity that mystifies common sense. There are so many factors that can come into play, as well; refraction index of epoxy, grain size and type of phosphor, temperature, die package, reflectors and optics (frequency dependence between Crown and Flint glass?), etc.
