You are keying into some great points here.

The energy recovered by a turbo is not entirely a free lunch. A turbocharger gets some of its energy "for free" and some of it not so free.

To the extent that the turbo is acting like a turbine (extracting energy by dropping temperature and pressure across the turbine blades), you are recovering that energy "for free".

However, to the extent that the turbo appears as additional back-pressure to the engine as each cylinder's exhaust valve opens, that portion of the energy is not had "for free".

Theory tells us that the amount of energy left to be extracted from exhaust gas is proportional to how much hotter it is than the ambient air temperature (even 1 degree means there is energy left in the exhaust).

However, every practical Carnot-cycle heat engine (steam, piston ICE, gas turbine, etc) ever manufactured leaves some energy on the table.

Practically, the process of extracting additional energy from the exhaust means running it through another "stage" of the engine (e.g. an additional ring of turbine blades in a turbine or an additional cylinder in a compound steam engine).

But here's the rub: Have you ever noticed that in every turbine of every jet engine, each successive ring of blades is physically larger in diameter than the one before it? And in a compound steam engine, each additional cylinder is larger than the one before it?

This is because the process of extracting energy from the exhaust requires allowing the gas to expand, requiring that the next stage be even larger in order to extract additional energy.

So in any practical engine, you reach a point of compromise where you decide that adding another stage is either too expensive, adds too much weight (or perhaps adds just enough friction as as to be counter-productive!) that it isn't worth it to chase after that last few percent of heat energy left in the exhaust.

Edit: This is also why you see the advent of combined cycle power plants. At a certain point, whatever heat is left in the exhaust is more practically used to provide heated water, than to try and convert it to kinetic (and then electrical) energy.

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

I actually didn't realise that the energy extracted by a turbocharger, more than any residual gas expansion from still-burning fuel (if any), is also dropping the temperature of the exhaust gases. So we are extracting some of the heat energy using a turbo. neat. Yes I take your point on diminishing returns. Still it seems that there is quite a big chunk of energy otherwise being thrown away, and turb[os/ines] are getting better and better at harvesting it.

Right. Yes. I believe I said that here:

    powered by exhaust gasses, which is known as a "turbocharger"

Yes, a lot of energy goes out the exhaust and turbochargers use some of it to compress air for the intake. Even with that there's still energy wasted out the exhaust. If it is hot and makes noise there's energy going out the exhaust. Principle of Conservation of Energy.

At the most basic level thermodynamic machines are about max delta T.