To your point about the increasing blade size, this is to allow the gas to decompress, however its less about extracting more energy and more about using the en

To your point about the increasing blade size, this is to allow the gas to decompress, however its less about extracting more energy and more about using the energy in the gas to keep it moving out the rear. One of the biggest problems with gas turbines is that theres nothing to stop the flow from reversing if the (intake pressure - forward momentum of the gas stream) is at a lower energy state than the exhaust. When this does happen you get what is known as a compressor stall. This is dangerous and costly in aviation (11 mil of overhaul for a GE90-115) and so a little less effiency is the compromise. You could run 2 stages of the same size of turbine blade but that would be dancing with the devil. Also, just to add to your comment, another form of energy that you get for free from a turbo application is harnessing the sound pulses from the exhaust. You wouldn't think it's much but all you have to do is compare the F1 V10 vs the V6T https://www.youtube.com/watch?v=jS4Dh_EAfJI https://www.youtube.com/watch?v=jS4Dh_EAfJI