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I think I just debunked my own myth.
The specific heat rato for air hovers around 1.4, whereas CO2 is around 1.28. doing some simple math points to needing a much higher compression ratio to get the same efficiency. For an example, to get the same thermodynamic efficiency as an air fed ICE with an 11:1 CR we'd need over a 30:1 CR to get the same efficiency in a CO2 fed ICE. Water vapor also doesn't help much with it's 1.3 specific heat ratio. The only thing I haven't factored in is if there'd be an efficiency benefit to running nearly as much liquid water injection as we want since lots of water condensation would be available in this theoretical engine.
Helium would be a great working fluid in such an engine with it's 1.5 specific heat ratio. The problem is now we'd have to very efficiently separate the water and CO2 out of the helium in order to make it work as an ICE.
So as it stands now, such an engine would be very inefficiency and cause a lot of CO2 emissions in an effort to remove NOx emissions.
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