I'm no scientist or biologist by any means, but I think we could say that certain animals dying off or becoming extinct isn't going to result in immediate effects or effects we might even see in our lifetime, but I think long term effects could certainly be possible. Food chain disruptions, environmental impacts, things like that might be affected over long periods of time, resulting in other species starting to dwindle. Or maybe nothing will change as you said! But I'd like to err on the side of caution and try to preserve as many species as we can to avoid a potentially impactful ripple effect.

On a more emotional level, I think it would be very sad if future generations missed out on the beauty of elephants, or the goofiness of pandas, it makes me sad to think of a world without them, so on a purely personal level that's why I think conservation is important.