Nikon began the trend with the 36.3-megapixel D800E early in 2012 (the D800E actually has half of a low-pass filter and cancels the effect; Nikon also offers the D800, with a weak low-pass filter).
"The full low-pass filter cannot be completely removed, because it would cause the focal plane to move; plus, the camera still needs to be able to reflect infrared light rays. Instead of making a single filter with one layer, Nikon decided to still use three layers, but with two layers canceling each other out."
That does not make sense, the part about the two filters canceling each other out. Nikon used a glass layer in place of the low-pass filter in order to maintain focus with the sensor at the same location in the camera body. The IR filter used on the sensor does not reflect Infrared, it absorbs it. A thick IR absorbing filter will blur light slightly, as it does "acts like" a weak Anti-Aliasing filter. When converting a Nikon Coolpix 950 to full-spectrum, I took out the IR absorbing glass and substituted clear glass to maintain focus.
Leica has never used an Anti-Aliasing filter in their rangefinder cameras. The thickness of the filter was a problem for handling non-retrofocus wide-angle lenses. The Leica M8 has a 0.5mm thick IR absorbing filter, the M9 has a 0.8mm absorbing IR filter. The images from the M8 are "more crisp" compared with the M9.
Reflection style "Dichroic filters" are used on very small and inexpensive sensors these days. They can also be used over the lens. They also reflect a portion of the RED spectrum. Hold one in sunlight to give the Cats something to chase around the house.