A substance at the supercritical state is considered a fluid -- something neither gas nor liquid. What is the scientific argument on why compressors and gas turbines are used in supercritical Brayton CO2 cycles instead of pumps?
Two reasons: larger volumetric flow rate and to avoid mechanical failure. Just because something is academically said to be "neither gas nor liquid" doesn't necessarily mean anything in a physical application. Also, you should appreciate that there is a theoretical difference between an open (e.g., turbine) and closed (e.g., cylinder and piston) system when calculating work. For a closed system W=∫pdV while for an open system W=∫Vdp In a boiler feed pump, such as you might find in a supercritical coal-fired power plant, p is quite large (4400 psia) but dV is small. The low pressure turbine is much larger than the high and intermediate pressure turbine in a modern steam power plant. The LP turbine provides about 45% of the total power, while the HP and IP combined provide about 55%. People think that because the pressure is large in the HP turbine that this should be doing most of the work, but it isn't. The LP turbine is much larger in size and the ∫Vdp is also large. While dp may be small across the LP turbine, V is huge. Dig deeper into the thermodynamics and you will understand the processes and machines better.