Firstly these are just my theories, feel free to tear them apart.
As I understand it the warm LEDs use a thicker, or more dense phosphor, which whilst absorbing more blue from the LED, attenuates it more in the thicker phosphor hence generally lower output.
So I would expect the cooler ones to benefit more from e.g. recycling from the collar, less attenuation of the blue from the less dense phosphor, then the returned light hits the front surface which is a more efficient place for it to be. I’d expect the overall tint to end up warmer, but if you just want the cooler brighter output I don’t see the blue light as being wasted, without recycling.
I think the shiny surface of the HIs may be a protective encapsulant for the phosphor surface and the bondwires. It wouldn’t be practical to sell a raw LED with exposed bond wire (handling damage). Hence the flat designs now available.
If of suitable refractive index, even though flat, it may also provide a matching function (refractive index) between the phosphor and air interfaces, much as the dome does. Which I think would reduce internal light recycling, but improve it from e.g. an external collar, encouraging the blue to escape or return.
Perhaps the phosphor underneath is already rough, which I think may be better.
Though I think an engineered textured surface could be best, and we are seeing this sort of thing nowadays.
I’ve thought about trying a silicone conformal coating on de-domed emitters to see what difference it makes, such as https://uk.rs-online.com/web/p/conformal-coatings/0494714/
But phosphors are already a suspension of the compounds in a silicone base, so maybe no point except for protection.
I think someone used to sell something similar called LED seal, at higher price.
I like to use conformal coat on circuit boards anyway (trained this way), though I prefer strippable acrylic based versions for that, when the temperature rating and inertness of silicone is not necessary…
That makes sense, and confirms DrJones ideas.