If TMP was a "visual reboot," than every movie was a "visual reboot," especially First Contact, and the term reboot is rendered even more meaningless than it already is.
If you want to call it anything, call it a sequel. It's a sequel to the TV show. It's the same people picking up a few years later. Same creator, same ship. They didn't "reboot" Kirk as an Admiral. The dude got a promotion. And they didn't make a new Enterprise and say "This is what the Enterprise really looks like." They said "The Enterprise has undergone a refit. An overhaul" which is still going on when the film starts. And if changing the uniforms constitutes a "visual reboot," Then TNG, DS9, and even Voyager were rebooted during their runs.
The only thing that was "reimagined" was the bumps on the Klingin foreheads, but they still fly the exact same ships as in TOS, and TAS, still wear the sash, still act all macho, etc.
Then TNG continued using the various ships used in the first six movies. When they(TNG) wanted to depict 23rd century interiors, they rebuilt them as they were and showed them on screen. When TNG wanted to depict SF uniforms from the Kirk era, they used the same ones.