Here is an example of using Red/Blue combo to grow plants. This is a $120 DIY fixture I designed for a friend for a Hydro grow (hot peppers). 660nm LEDs + Royal blues. Best growth either of us have ever seen. The picture of the plants is 1 month of growth since planting the seed. Blows away a 1000w MH and 1/10th the power, and this is because it is only the spectrum needed for photosynthesis, none of the extra "wasteful" spectrum like greens, yellows, and orange that white lights put out. I am just pointing out what is needed for photosynthesis, not trying to say one has to only use these LEDs. If a person wants it pleasing to the eyes obviously they will need whites as well, it is up to the individual to decide how many reds/blues they incorporate into their light according to how much growth they want vs how pleasing to the eyes it is.
I do not agree that reds/blues just = hair algae. That is a maintenance issue, not a light spectrum issue if your planted tank/refugium is being over run with hair algae. People have hair algae issues all the time with RB/CW combo LED lights which has almost no reds in the spectrum.
Looking at graph below, reds are not blocked by the ocean in lagoons to any real extent, and that is where most of the "plants" we use in a refugium come from, shallow waters. You have to go down 10 meters (30 feet), before red light starts to get filtered out by the ocean and since no one has a 30' deep tank at home that is really a non issue if your goal is to grow macro algae as quick as possible (not saying that is the OPs goal, just saying it would grow the best with the use of 660nm reds). Note: I am only talking about plants here, NOT corals, which do react very negatively when too much red light is added.
And finally, here is the spectrum output of Cool White, Neutral White, and Warm white LEDs. You can see the cool white LEDs really drop off in intensity once it hits the red spectrum (above 600nm) where as the warm whites provide quite a bit of the red spectrum, but also A LOT of orange and yellow spectrum so about 1/2 of the output of a warm white LED is wasted light in terms of photosynthesis. If the ideal ratio (according to a NASA study) is 6:1 red(660nm):blue(455nm) ratio for photosynthesis then you can see by the graphs you could never even get close to that ratio because all 3 of the LEDs put out a significant amount of royal blue spectrum as well. Even with warm white LEDs your only looking at a 1:1 ratio. Again, I am just pointing out what is required for the best possible growth of plants, of course plants will still grow with white light, just not nearly as well. If growth isn't a main concern then using all whites is fine.
Not trying to create an argument, just trying to give good information on how photosynthesis works.