Please allow us to earn mage tower recolors on other characters

There’s two different systems at work here:
Legion Artifact Appearances (from the Forge in your Class Hall)
and
Transmogrification collections (from the Transmog vendors/mounts etc)

Legion Artifact Appearances are unlocked per character, and selected from the Forge in your Class Hall.

Transmogrification collections are indeed account wide, and for the Legion Artifacts any appearance you have unlocked can also be used by other characters of the same class, spec dependent still.

For things like the Mage Tower color variations, and actually any of the color variations of the Legion Artifacts, that has to be unlocked by the character who has the first acquired the base appearance for that row (Classic, Upgraded, Valorous, War-Torn, Challenge or Hidden) in their Forge back in their Class Hall.

The limits on unlocking these were already relaxed during Legion (back in Patch 7.3), originally you needed to not only have the base appearance unlocked but also be using that appearance while doing the extra activities to unlock the new tint.
You don’t need to be using that appearance anymore, but you do still need to be on the character who has the base appearance unlocked in their Forge.

Once it is unlocked, then it’s going to be a part of your Transmog collection and available to others of the same class/spec to use.