Can't attach color profiles to documents created in the web version

When I create a document in the web version, it doesn't get a color profile.

When I later open that document in the desktop version, attach a color profile, make some changes, then save, the color profile doesn't stick. WHen I open the document again, the color profile is not there.

Saving a Cloud document is possible with a color profile, when I create the document in the desktop version. The color profile will stick when I open the document in the web version, but not the other way round.