You are treating ISO as part of exposure, so feel 'cheated' that, when set for the same shutter speed and aperture, the Fuji needs a higher ISO value (or to be boosted in post processing.
However, the exposure is the amount of light falling on the sensor, divided by the sensor area. It is therefore determined by the f number and the shutter speed, nothing else.
The ISO setting is not a 'noise' setting. Noise seems to increase as you increase the iso setting, because you increase the iso setting in low light, and low light causes noise.
ISO is just a way of making sure the brightness of the image matches what you want. If you wanted to, you could boost the image in post processing instead, and get very similar results.
With modern sensors, the amount of light is the main factor impacting noise. As a result, f5.6 at 1/500th on the Fuji will have roughly the same noise as f5.6 at 1/500th on the Nikon. The results may not be identical - some cameras do perform better in low light than others - but that has nothing to do with the iso setting.
In England, when they moved to the Gregorian calendar, they moved the calendar forward 11 days. There were riots by people who thought their lives had been cut short, chanting 'give us back our 11 days!' Worrying about the iso number is the same thing; if Fuji added a nought to every iso number on the dial, it wouldn't make a blind bit of difference to its performance, positively or negatively.
As for the different ISO standards, it isn't a question of iso 200 on the Fuji = iso 100 on the Nikon. Your results will differ depending on the scene and its highlights and shadow areas. If you want to play around, imaging resource in their camera reviews include a number of images with controlled lighting, so you can see how differently the cameras expose them. You will find a whole range of values, Nikon being on one extreme and Fuji being on the other. Which is better is more or less irrelevant, as it doesn't influence the output.
I agree in your statements above.
The question is where it leaves you when light is marginal and you need to keep the shutter speed up.
I am ok with ignoring the iso value in itself, but when you are pushing the sensor towards its limits at the high iso end you will inevitably end with a poorer quality image.
Fast action requires a high shutter speed.
There is no substitute for that.
You set the aperture and shutter speed your shot requires, or your camera allows.
That leaves you with a higher iso value on the Fuji, or with having to push the Fuji file in post processing. The question is whether that is a disadvantage.
The answer to that is no. The iso is abitrary, and doesn't amount to a measure of the amount of noise in a photograph. Take this example, from the DP comparison tool, first with JPEGs:

JPEG test
Look at the words on the colour wheel - do you see how blurry the Nikon image is? That is the JPEG noise reduction kicking in at iso 6400. However, the Fuji is at iso 12800, and suffers less. It is more on par with the full frame cameras at the bottom at iso 12800.
However, that is misleading, as the Fuji image had more exposure. Have a look at the situation in RAW:

RAW test
With an equal amount of exposure, and with the image adjusted to the same brightness in post processing, the Fuji is now more or less equal with the Nikon (it has less colour noise due to the X-trans array, but doesn't have less overall). The full frame cameras now pull ahead, as you would expect.
So if you are out with the Fuji, just let the iso climb higher than you normally would. You will not suffer from more noise overall.