First, we're dealing with plants, so photosynthetic efficiency is 5% if you're lucky (photosynthesis sucks for efficiency - chlorophyll is green, not black for a start). Sure, that's mostly for producing sugars and amino acids, not lipids, but that's what the algae do at the start of their life cycle. Given that the trial farms are mostly in the open in temperate or tropical climates, there's enough sunlight and looking at photosynthesis isn't going to make any difference (Solazyme use azooxanthellae algae that get their energy from sugar and not the sun, but I think that's mistake - we'll see how it goes)
Second a load of work has been and is still being done to see when and how much nutrient stress to place the algae and what else, like calcium carbonate, to add at just the right time to maximize lipid growth and whether any of a couple of hundred strains (a small proportion of all existing, I agree, but they're the ones that look most likely to produce over 45% mass lipids) has properties that make it worth spending an extra day increasing the cell size before nutrient stress to make lipids. In general, make lipid as soon as possible is the finding - the extra cell size generally means proportionately less lipid
Third, Amino acid market? google spirulina protein powder. As a western nutritional supplement it's been around for a few decades and as a part of the diet in some parts of the developing world, the dried algae has been consumed to provide most of the protein for generations. Some poor parts of India have the longest standing algae farms - basic raceways making food for people. This gives you some idea
Fourth, I agree about reducing the use of fertilizer and not only because of efficiency of utilization in algal photosynthesis (I don't even know if it is), but because farming generally squirts fertilizer onto ground and hopes some of it will be used before being rained away whereas algae farms put fertilizer into the water knowing that it will all be used. Getting most people to eat it as a major part of their diet or farmers to use it as feed will require a bit of a cultural shift, but the tech has been in place for ages
Fifth, water will probably be waste or reused in a PBR so no or minimal ongoing cost, NPK could well be waste if an algae plant also treats sewage so no cost. The carbon boost could be provided by other sources of carbon - calcium carbonate is a waste product of water desalination plants, so would be a good option in some cases. I don't see that photosynthetic efficiency is a game changer unless you're thinking of growing in the arctic circle, but area of land or water (as in Jonathan Trent's omega project) is going to have to be big.