The stator fins also make the jetdrive more efficient...
Here's how I explain this to people.
Imagine a nut screwed onto a bolt. If you turn the nut, it moves along the bolt. But if you turn the bolt, that also makes the nut move. In other words, all you need is relative motion between the two. Together, the bolt and nut are a system that converts rotational motion to linear motion.
When a propeller "screws" its way through the water, some of the energy is converted into linear energy that pushes the water stream (and thus pushes the hull forward). But a lot of the energy is lost to rotational motion of the water. You can see this if you study the water coming off a traditional exposed propeller - you'll see the water swirling around back there. That rotational motion does not help push the hull forward, so it is wasted.
But in a jetdrive, you have the opportunity to recapture some of that rotational energy via the stator. Yes, the stator supports the rear of the impeller shaft - but if that were its only job those vanes would simply be straight for minimal hydraulic resistance (friction). Instead, you'll notice that the vanes are slanted. Thinking back to the bolt-nut example above... when the rotating water stream (the "bolt") encounters those tilted stator vanes (the "nut"), the vanes are moved along the water stream. The water moves the vanes, the vanes move the stator, the stator moves the powerplant, and thus the energy is recaptured and used to propel the hull.
So the stator's vanes convert some of that rotational motion into linear motion to help move the hull. It's not 100% efficient on these simple jetdrives because the optimum angle for the stator vanes changes with varying impeller RPM, water velocity through the drive, etc. More complex and expensive jetdrives (on larger boats) have adjustable stator vanes, like variable pitch aircraft propellers, to optimize for those varying conditions.
There's quite a bit more going on in a hydraulic jetdrive than first meets the eye! [grin]