tosefos brings examples of how andrati means of a living king. how does rashi know that andrati is of a deceased beloved king?
yehuda hamer, boredimore, merryland
The Ritva learns like Rashi, and the Hagahah there (note 17) points out that later in the same Dibur he will cite the Yerushalmi who holds like that.
I think that the reason for this is because of the aspect of worship over which Rebbi Meir and the Rabbanan argue. And whereas they would worship the bust of a king that was no longer alive either on the day that he died or on his birthday, as the Ritva explains, they would not do this with the bust of a live king (which was rather a symbol of honor than of worship).
Tosfos does indeed prove that the kings would erect busts of themselves even when they were alive, but who says that they were meant to be worshipped?
R. Eliezer Chrysler