Completing the set of former Imperial palaces that I've visited, the question regarding Kyoto was a different one, when, after the Meiji Revolution, the throne of Japan was moved to Tokyo, ending Kyoto's 1000-year tenure as Imperial capital. The answer came swiftly: keep it. After all, it had only been rebuilt in 1855, fires having destroyed the palace multiple times in the Edo period alone.
The Shishinden throne hall, with its courtyard and traditional tachibana orange and sakura cherry trees either side of its grand staircase, was used for the coronations of Emperors Taishô and Shôwa (Hirohito) in 1915 and 1928, but since the accession of Emperor Akihito in 1989, coronations have been held at the active Imperial Palace in Tokyo.
Today, the palace is preserved and can be visited for free, albeit on a fixed tour route. Only the exterior of the buildings can be accessed, still allowing good views of the Shishinden and the gardens to the East of the palace.