I managed to fix this issue by tweaking the registry.
First, I followed the instructions here to remove the even more annoying item that is created in the "Devices and drives" list.
Next, to actually remove the icon from "Quick access" in the Navigation pane:
1. Open explorer and unpin "iCloud Photos" from the "Quick access" by right clicking on it and choosing "Unpin from Quick access".
2. Open the Registry Editor: press "Windows-Key + R", type "regedit" and then "OK".
3. Press "Ctrl + F" and type the string "{F0D63F85-37EC-4097-B30D-61B4A8917118}" (it suffices to only check the "Keys" option). Click on "Find Next".
4. Once found, right click the registry key and choose "Rename". Change the name to "{F0D63F85-37EC-4097-B30D-61B4A8917119}". (I chose to rename it instead of deleting it, since I am no expert and did not want to risk it. Perhaps someone else will try deleting and see if it works.)
5. Press "F3" to find the next ocurrence of the string, and repeat step 3. Sometimes the editor will complain and say it cannot rename it, in which case ignore it as it will later change automatically. Repeat this until you reach the end of the registry.
6. Close the registry. (Optionally re-open the registry editor and search again - there should be no ocurrences of the key "{F0D63F85-37EC-4097-B30D-61B4A8917118}").
7. Open "iCloud". I had custom photos directories for "Downloads", "Uploads" and "Shared", but the registry change for some reason resetted these values to the default. If this is your case simply click "Options" next to "Photos" and make sure to change the directories to your custom preferences. These will be saved from then on.
That's it. When you restart, or open "iCloud" it should no longer create the annoying and arrogant "Quick access" pin in the Navigation pane.
Hope this helps some people.
