<nods>
I am surprised by the extent of the lossiness of *PON splitters . . . two of 1:128, back to back, and its getting close to the higher (45 dB) attenuation that I was pondering in my hypothetical experiment.
It's inevitable and unavoidable. The light is being split each time so photon count per port is halved, power is photon count so is halved. Attenuation on optics is a function of leakage / absorption of photons which is how it can be reduced by reducing leakage from the fibre core and why multimode has much lower range: larger fibre core, light bounces more and at more acute angles within the core, more photons lost per metre. As far as splits go 1:2 = 3 dB, 1:4 = 2 * 1:2 splits per port = 6 dB, 1:8 = 3 * 1:2 splits = 9 dB, 1:16 = 4 * 1:2 splits = 12 dB, etc. To avoid this would need amplifiers making the network no longer passive.
Can work out the loss easily enough by using the split ratio, use that larger number, take it log 2 and multiply by 3. 1:128 = 128 log 2 = 7. 7 * 3 = 21 dB.