You're fundamentally right, because the equation you've given has the sign reversed. The adjustment should go on the left side of the equals sign, not the right side; if you want to move it to the right side, it needs to be subtracted. Or, to answer the title question: it doesn't.
But, I think part of the confusion comes from looking at what EV is meant for in reverse as well.
You say:
the lower the EV value, the more exposed (bright) the image is
This is looking at it backwards. A better way to put it would be: The lower the EV value, the more you need to use more-light-gathering and more-sensitive camera settings to get a proper exposure.
The goal is to get images with the same brightness ("correct exposure") regardless of the actual level of light in the scene. When we're out in the world, our eyes and brain adjust and normalize the light levels — sometimes we're aware that it's very dark or very bright, but overall, we just adjust. We can't adjust when looking at a fixed photograph, though: the exposure is whatever it is.
So, exposure value is a tool for helping to get this right. In modern cameras, of course, it's all done with automatic metering (even in manual mode, we usually follow what the meter says as a guideline). But if the meter weren't built in, you could use readings of the "exposure value" of the scene (or, just estimate, once you're familiar enough) to set the camera settings so that you get a nicely exposed image.
A higher exposure value represents a brighter scene. At ISO 100, bright sunlight is around EV 16, an overcast day more like EV 12, a home interior at night is something like EV 5, and starlight around negative 6 EV. From this, you can figure out what shutter speed, aperture, and ISO you'll need.
Although one might look at the right side of the equation and say that a certain aperture and shutter speed "produce" a certain EV, it's more normal to look at the EV of a scene and then decide what shutter and aperture are required to get the correct exposure. (Where "correct" means "basically average" — you're free to expose in a higher or lower key if you prefer!)
The "EV compensation" adjustment on modern cameras is meant to work with this. By dialing in negative -1 EV, you're telling the camera "Your meter says the EV is N, but please calculate exposure settings as if it were a one stop darker". Or by dialing in +1 EV, you tell it that you want the scene exposed one stop more brightly. This can be used to correct for metering errors or simply for artistic preference.
So, where does ISO come into this? Simply put, each stop of ISO (that is, each doubling, from 100 to 200 or from 200 to 400 or from 400 to 800, and so on) shifts the scale by 1. (log₂(S/100) is just a fancy way of saying that.)
You can also rearrange the formula into:
log₂(N²/(t×(S/100)))
if you like — it's another way of looking at the same thing, and in fact a mathematical way of expressing two slightly different definitions of the word "exposure", as explained in this other answer.
Or, you can write it out with all the terms separate, which I think is most clear of all:
EV = log₂(N²) + log₂(1/t) - log₂(100/S)
Because that's really how one is meant to think about it in the real world. Or rather, one is meant to think:
EV = aperture + shutter - ISO
and not worry about all of the logarithms.
