Your description of the battle system in Golden Sun is exactly how I feel about GF summoning in FF8. Takes forever to watch, you can do it anytime, and the battle is over. Makes the battles completely uninteresting and inconsequential, and combined with their length, makes the game completely boring.
The problem with Fire Emblem characters dying is that you then
don't get to see their involvement in the story. No one wants to play through the game 10 different times to get every character's reaction to the plot events, so you end up with people just resetting the game whenever someone dies. It really makes the game annoying to play through and limits the scope of the battles. In a game like Advance Wars, you can have larger confrontations with more going on because it isn't the end of the world when you lose a unit. Instead of spending hours analyzing every possible move that could be made, you can just formulate a general strategy and execute it. Losing a unit is OK if your strategy ends with you coming out on top.
Vudu, what you described is, IMO, not a feature of the game.
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once your characters have increased several levels, you are in a real pickle if a unit dies and you choose not to restart the level.
Nobody wants to lose a character that they've spent time building up, it's completely frustrating. Even worse, if you are having particular trouble making it through a long battle, and you finally end up winning but without one of your stronger characters, then you save your game and end up screwed because you're missing a character, you basically end up stuck and have to restart the entire game if you want to get unstuck. That's not a good thing, it's a problem with the game design. You're supposed to be reward players, not penalize them.