Interestingly, a good portion of the Imperial Palace -did- burn down due to fire-bombing, though apparently not from deliberately being targeted. Richard Frank discusses this in Downfall (an excellent resource for anyone who's interested in the end of the Pacific war.)

One of the potential uses of the atomic bomb was to attack the imperial palace directly - i.e. to kill the Emperor. It was ultimately rejected as a recommendation for the targeting of the atomic bombs because, as the US understood it, it would not have made a particular difference in the Japanese war effort (the Emperor was a symbol, but not involved in the day-to-day running of the government; his intervention to break the deadlock and surrender after the atomic bombings was largely unprecedented.) In addition, Tokyo wasn't really a good target for the atomic bomb in general at that point - pretty much anything we'd wanted to bomb was already thoroughly bombed.

So there wasn't a particular decision to attempt to kill the Emperor, though it was mulled over - but they didn't take particular care NOT to kill him and with different luck it might well have happened.