If we suddenly had a real starship, able to travel as far and fast as the ones on TV, and with no relativity "time dilation" problems, would you volunteer for a multi-year mission?
You'd miss a lot of people and things back home, but you'd get out there and see the galaxy.
It's hard to say what I'd decide. On the one hand, yeah, let's blow this pop stand. But on the other hand, the solar systems you'd explore might all be lifeless. And if you did find life finally, it might be some mold and bacteria on a slimy planet with nothing much to offer.
And your life on a starship might be even more confining and limiting than the daily grind you have now. It might be like working in an office building you never get to step outside of.
But I think there'd be no shortage of volunteers.