In a way, even if we don't live, we have seen the Restoration already. Its outlines may be indistinct, but we have seen it.
My reason to want to live to see the Restoration is frankly pretty personal. I feel I've wasted a lot of time and I want to be useful somehow, to do something for God, but I don't know what to do in the present moment when everything seems pointless.
But ultimately, the goal is not to see the Restoration, it's to see God in heaven. The Restoration will not be like a Renaissance Faire with everyone dancing and singing, it will be a medieval-type world with everyone working hard on farms and doing back-breaking labor, trying to rebuild the world. True joy is found in heaven, in the presence of God. The Restoration is still an earthly event, no matter how glorious, and this is still a fallen world.
If I do live to see the Restoration, I will have undergone hell and will very weary, not the relatively bright-eyed and bushy-tailed Raoul of today ( despite that my life is already grisly, it takes a lot to beat me down ). I just feel like my life is incomplete at the moment, I want to be of service and work off some purgatory time -- never in my life have I FIT anywhere and before I die I hope I do -- but it's all up to God.