There is some confusion in the 'wants'!...
In Av mode, everybody easily understands that you fix the aperture (I assume based on DOF considerations) and in Tv mode you fix the shutter speed (based on subject or shooter movement considerations). This has carried over from the film days. Then, you couldn't change the ISO, it was set by the film manufacturer.
However, it is clearly understood that occasionally you need to overexpose/underexpose the photo (snow scenes, beach, sunset etc etc).
For the automatic modes, Canon has provided the EC function.
However, until recently, in M mode the photographer sets the aperture and the shutter speed (and the ISO). There is no automation needed in M, the same way you set aperture, speed (or ISO) you can set them the desired number of stops higher or lower.
However, Canon made another concession. They gave you an extra automatic mode where you set aperture (based in DOF considerations, or maybe lens performance) shutter speed (based again on movement requirements) but allowing the ISO to float in an auto ISO mode. This created such hue and cry because now you have an automatic mode that you cannot apply exposure compensation!
Oh the shame!
(Well, actually you can, in a way... you can use exposure bracketing, with the bracketing being the EC you want. You shoot 3 pictures, one useless, one properly exposed to 12% gray and one exposed the way you want...). A bit of a waste, but oh well...