Since being alive is what most people cherish, time before birth is an unconscious countdown to this nice state. Whereas time before death is a conscious countdown to have it taken from you.

That both times are a "period where you're not alive" isn't enough to make people treat them equally. It's the difference in context that matters. Else one might ask "why people aren't afraid of kitchen knives when they're cooking, but are when a serial killer charges at them with one?"

People wouldn't give a fuck about the time after their death if it was in the past, like their time before birth always is while they are alive.

Because the time before their birth is not in the future?