Just because you're aro or aroace doesn't mean you don't understand heartache and loss. When we empathize with fictional characters, is it because we've been through exactly what they've been through? Doubtful, because then fantasy wouldn't exist. But we've had similar emotions, so it resonates.
I don't really see why songs would be any different.
It's one some people who both identify as aromantic and asexual use. I've seen some people who prefer it to using the flags for both of those things separately because they preferred to think of their orientation as a singular thing rather than breaking it down into sexual and romantic attraction, though not everyone that uses it rather than both the ace and aro flags it does so for that reason.