In a group interview with World of Warcraft game director Ion Hazzikostas, it was revealed that Blizzard is planning on making gray and white items able to be used as transmog. This would be awesome as there are a ton of unique white and gray items.
The exact quote as posted on Wowhead is below:
“Ongoing expansion and customization of it is something we are looking to do certainly by Dragonflight, possibly before then is rolling a lot of the white and grey quality items into the transmog system so that you can choose from a lot of simpler, humbler civilian attire-type looks. We want to keep adding in more options for customization and self-expression.”
So it seems like this could even happen before Dragonflight, perhaps even for the 9.2.5 patch but I wouldn’t be surprised if it was later on.