Z Screen vs Rest of the World

I thought the ICC profile is a representation of the device's properties and how it shows/produces colors. In my case the normal blue on this device would be shown more as purple if not adjusted by the program generating the color (Photshop/Lightroom).

 

Well, yes, the profile is a high level description.
However, in the practical application of the profile, and given that all RGB values are already taken, the only way the driver can adjust the colours to fit the profile is by compressing and removing some colours so others can be shifted there.

An example: Let's say that the display shows #4E30A7 too saturated, and need to shift it to #4C32A2. That shift alone reduces the available red values for colours dimmer than this by 2, green values brighter than this by 2, and blue values dimmer than this by 5.

You get more correct colours, but fewer of them.

For a 6-bit display (like on the Z), it doesn't matter as much because the RGB values have to be compressed anyhow -- unless the shift in colour is rather high, the reduction caused by the 8-6 bit display conversion is going to mask the reduction caused by the profile adjustment.
In practice, in addition to the most saturated values being shifted down, and overall "truer" colours, you may see slightly more dithering.

 

First I have to correct myself, ICC profiles do not only work in apps like Photoshop, they also work for Windows 7.

@travar
Could you please try something on your notebook and let me know if it improves your blue neo color situation?
- unzip the file in my attachment
- copy the icc file to this folder on your computer:
C:\Windows\System32\spool\drivers\color
- go to Control Panel > Color Management > Advanced, click on change System Defaults > Advanced > check Use Windows display calibration, click Close
- In Color Management > Devices select Display, check use my settings for this device, click on Add, select the Sony_6700K....... profile you put in the folder above and click OK
- it should've marked this profile as Default, click close

Now you should already see a difference in the colors.

The profile was created by i1Display 2 with target 6500K, 110cd/m2, Gamma 2.2, brightness was set to 64% (three steps down from 100%).