Apparently hardware calibration has some benefits, namely that it doesn't rely on ICC profiles.
That has nothing to do with it.
All color management is based on icc profiles, but calibration is not color management. You're confusing calibration and profiling.
Calibration is just a basic linear correction of the display's response. It can be done internally in the monitor ("hardware" based), or through the video card ("software" based).
Color management enters with the display profile. That's a complete description of how the display behaves, in its current (calibrated or not) state. The monitor profile is three-dimensional and has a much higher precision level.
The advantage of hardware calibration is that the monitor's internal LUT operates at much higher bit depth, while the video card is an 8-bit pipeline. Thus you eliminate the risk of color banding and other artifacts, as well as giving much better control over the white point.
(EDIT: Although in some sense it's correct, because the video card LUT is usually stored inside the profile. That's really just because it's a convenient place to keep it, being display specific, but not because it has anything functionally to do with the profile. They're still separate and serve different purposes. With hardware calibration, it's stored in the display and so you could say that it doesn't rely on the profile. But this is just semantics, really...)