The idea of a "bloom booster" was tied to extra phosphorus by marketers of fertilizer
many years ago.
Back then, bark was pretty much the basis of all potting media formulations, and it was noted that over time, plants grew less-strongly. Scientific work determined that the microorganisms that consume the wood as it decomposed also consume a lot of nitrogen. That led to the development of high-nitrogen fertilizers like Mir-Acid (30-10-10), developed by Dr. O. Wesley Davidson of Rutgers U., to compensate. Unfortunately, it was found that the use of high-nitrogen fertilizers also led to a reduction in blooming.
The fertilizer manufacturers then added inexpensive phosphorus compounds in order to dilute the nitrogen, bringing it back to a reasonable level. That's where the marketing folks got involved, which led to the recommended regimen of feeding the high-nitrogen blend during the "growth phase" of a plant, then switching to a "bloom booster" well in advance of the plant's blooming period (i.e., "undoing" the nutritional overloading of nitrogen).
Keep in mind that back when a lot of this was being studied, most cultivated orchids were cattleyas and cymbidiums for the cut-flower industry, so the timing of blooming was reasonably fixed - especially compared to the variability of today's complex hybrids and much broader selection of genera - so such a treatment was a viable option, and the "booster" hype was an easy sell.
A few years ago, Dr. Bill Argo challenged the booster myth and the associated feeding regimen, so did some digging into the specific nutritional needs of orchids, and developed a formula that could be used at all times and would completely satisfy the needs of the plants. He did some testing with the assistance of folks at his alma mater, Michigan State University, and that formula is now marketed as the "MSU Fertilizer" for pure water.
My own experience with it (every watering for the last 5 years) backs that up.
I have compiled a bit more in this arena on my website:
Plant Boosters