When the promise is "nothing ever changes unless you change it", then your motivations will change pretty substantially.
I also you think both your assumption and the reasoning behind it are wrong. Humanity as a whole is the opposite of apathetic, it's boiling with life. There are occasional pockets of apathy here and there, but they never last long.
And the reason why people on average are active and risk-taking is because their life is worth nothing. You lose your life no matter what you do, so you can as well do something good. And if you want to see change in your lifetime you better hurry up.
No one would risk their precious eternal lives if aging is gone. And if you want change you can safely wait forever without taking risks, maybe a meteor will fall in 10000 years and change things — who knows!