Very few things have been entirely removed from League of Legends in the game's decade-plus history. Typically, Riot Games only makes improvements and additions, although there have sometimes been cuts in certain features.
This has been the case with login screens and animated splash art, which seem to have disappeared forever with one of the large client updates.--p-ze received.
Riot Games' Recovered Tradition
Over the last few years, community complaints about the loss of this type of content have been common. However, Riot has declined to implement these systems in the new version of the game client and the login screen, due to the difficulty and perhaps a focus elsewhere.
However, that doesn't seem to be the case in China, where animated splash art has recently appeared in the client for the occasion of the Coven event .
Unfortunately, these changes aren't permanent, instead just part of the promotional campaign for the event in China and only visible on its website. However, it is an interesting first step, one that allows us to see this type of work again, officially.
While many fans would like to see animated splash art return in the West, the Chinese server often gets content that remains exclusive there. In reality, it's unlikely we'll ever see animated splash art in the West as a permanent feature.