Which is super inefficient! Most of it will be absorbed and some scattered back into the reflector and then back into the LED… I find it hard to believe that this has a meaningful impact.

You will probably get higher performance by using a collar which only reflects blue light and absorbs the rest of the spectrum. This would keep the phosphor cooler and you might reflect 3-4% more of the blue part.

You could try proving your point by using the collar with a very warm (<3000K) led. I predict a very small gain.