Three cases

Case 1, insulated (adiabatic) compression

All work is exported. Compression work is cancelled out between cycles.

All unused fuel heat can be recycled except for the heat of compression, so its advantageous to have lower compression ratio.

The unused, unrecycled heat, equivalent to the heat of compression, is exhausted.

The example shows fuel heat equal to ambient heat, so thermal ratio is 50%, and efficiency is 50%.

This would tend to support the "limit" thesis.

Case 2, uninsulated (isothermal) compression

All work is exported. Compression work is still cancelled out between cycles.

All unused heat would appear to be recycled, except that the act of isothermalally compressing discards a portion of heat equal to the work of isothermal compression. This is less heat than adiabatic compression, but still discarded.

The unused, unrecycled heat, equivalent to the heat of compression, is exhausted during the compression.

The example shows fuel heat equal to the previous cases heat, for comparison. Again, the thermal ratio and efficiency are equal, and in this case a bit over 50% (specifically 26/46).

This would also tend to support the "limit" thesis.

Case 3, no compression. This method has two issues. The primary issue is that it cannot export a sizable fraction of the work done. A second issue, is that the heat of expansion of the ambient temperature air, must still be replaced. Since depicted is 1 unit ambient plus 1 unit fuel, just the replacement makes this 50% efficient, supporting the idea that efficiency is limited to the temperature ratio. The exportability issue makes this about 25% efficient. It is noteworthy that 25% is still more efficient than any car on the road at city speed.