Ignore the Media White Point in Scanner Profiles
I want to profile my scanner using an IT8.7/2 chart. Analyzing the ICC profile I generated it shows that the Media White Point is close to D65 illuminant (6501K). What does this mean?
For reflection scanners, nothing. And the Media White Point in an ICC scanner profile is not that of the scanner's illuminant.
Reflection scanner profiles convert "rgb" values from a scanner to D50 Lab values. Always. These are then typically converted to a standard profile such as sRGB or ProPhoto RGB by the application using the scanner profile. D50 is the common reference for ICC profiles. While "Media White Point" has a critical meaning for operations such as printing, this is because the printer paper is never a perfect white and the white point of unprinted paper or unexposed photo paper must be measured and taken into account for calorimetrically accurate printing.
Scanner profiles, on the other hand, not only don't use this information, they have to no way to determine it. Scanner profiles are made from the scanner RGB data together with the D50 Lab data that is supplied for the IT8 scan target. Nothing else is needed or available. For instance here is the spectrum of the illuminant measured from my Epson V850 scanner. It's not anywhere close to D50 or D65 yet the Media White Point in an XRite IT8 profile is D50.

For accurate reflection scanning, it simply doesn't matter what the scanner's illuminant, alone, is. What does matter is the illuminant, multiplied by the RGB filters' and sensor response at each wavelength. Ideally, they should match, in a linear, combinatorial sense, the CIE D50 color matching functions. This allows high quality profile creation.
Does it mean that whenever I apply this profile to an image it will have a D65 white point?
No. Applying a profile to a scanner image results in Lab values based on D50 regardless of what the Media White Point is set to.
Other Problems with Scanners Profiles Can't Fix
Two significant sources of error are intrinsic to scanners. Metameric Failure Error, and Large Areas Spacial Crosstalk.
Metameric Failure Errors occur when two colors that are visually the same but significantly differ in spectra, have different colors when scanned. IK have run across this when comparing scans of a ColorChecker card and the same colors printed. Even though the measured colors are within 1 deltaE of each other with a spectrophotometer, the colors of the scans differ with the two images varying by as much as 9 deltaE. That said, scanners can produce quite accurate scans if they are profiled from charts that use similar media. For instance scanning chemical color prints will produce the best scans when profiles are made from IT8 charts using the same chemical color process. Similarly good quality can be achieved with inkjet printed IT8 charts and these profiles are excellent for CYM printed materials. I've found remarkable consistency across multiple printers with the same inkjet chart profile. However, large errors still occur scanning natural colors or pigments used, for instance for artwork.
Large Area Spacial Crosstalk occurs when nearby light from a scanned object bounces off near structures on the scanner and adds light to the points being scanned. Since this process is linear it can be estimated mathematically. I have seen as much as a delta E of 8 occur with an Epson V850. A detailed description (and program to correct it) is here.