The clear payoff is: as far as we've seen, life only exists on one place in the universe, so it makes sense to spread it out. Not putting all your eggs in one basket. If you can't see how that's an inherently good idea, I'm not really sure I'll be able to convince you.
Your post is thinking on timescales of millennia, at the longest. We know the sun will burn out in a few billion years. We know another 'ice age' is coming in a few thousand years - the entirety of human civilization cropped up in the 10,000 years since the last major ice sheet retreated. We know earth will have some kind of natural disaster, whether it's tectonics or bombardment, and we may not be powerful enough to manage it when it happens. This knowledge alone is enough to justify the cost of trying to get off this planet.
>It's a helluva lot easier to apply our intelligence to normal prosaic things here like taking care of the environment, than to building interstellar spaceships that can colonize other planets.
"We should fix all the problems here on earth." Every time the idea of building in space comes up. As if we're capable of fixing all our problems on earth linearly and in order before moving on to space, and as if there are only enough resources for fixing the things you think are important. This is the classic, "this solution won't fix the problems we're currently not fixing, so we shouldn't do anything until those problems get fixed."