Aragorn did not succumb to fear; Arwen did. That is the tragedy.
In what sense did Arwen succumb to fear? She didn't try to go to the underdying lands like the Numenorians did. She didn't kill herself like Denethor. In the end, she abided by her choice, though she found it a bitter one. I don't see a tragedy here, not if Aragorn is right about the "gift to men".