I actually completely agree with this.
Most deaths in the FF series rarely impacted me beyond the annoyance of losing a character who suddenly became useful (Tellah and General Leo) or was someone I didn't really care about. Death in the FF series never really got to me like it has in other game series. Even the few characters I do care about usually go out in such a fashion that I feel it helps define them as a character. So its hard to get weepy when it was done well for story purposes.
Though there is one exception and that's possibly Cid from FFVI, only because its a death that is left in the players hands and failing grants you access to one of the most memorable scenes from the game. Just the simple fact you can prevent the death if you work hard enough made it have a bigger impact on me.