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If you imagine the hot gas expanding through the first turbine, it imparts some torque to the shaft and as it departs the blades it is now *rotating at the same speed* as the shaft. So you started with a high pressure annular (doughnut) bit of gas and end with a slightly lower pressure doughnut that is rotating. If you want to use the doughnut of gas on another set of blades you need to get the gas to stop rotating. The fixed blades take away the rotation at the expense of a little bit more pressure. The now-no-longer-rotating gas appears “fresh” at the face of the next turbine, with the ability to trade some more pressure for torque.
What it comes down to is that the “ideal” propellor/fan/turbine is infinitely thin. A design like this approximates this with a series of thin rotating and static blades.
TL;DR rotating gas can’t impart torque on subsequent turbine stages.