Space missions certainly take a lot of time, resources and money, but not all of it disappears into space. Everyone working on the mission is paid wages or salaries, and that money is spent in local stores, bars, and so on, and then gets spent again on other things. The money isn't blasted into space, it stays right here on Earth. A fair amount of that money goes back to the government in the form of taxes, too, of course.
Similarly, all the resources such as metal, plastics, fuel, electronic and mechanical components, and the raw materials that those components are made from, all provide employment for the people producing them, and once again, that money stays here on Earth, and goes around and around, as it always does.
The only thing that actually leaves Earth when a spacecraft is launched is the payload, whether it's a satellite, food and other supplies for the crews of the International Space Station, or a space vehicle that travels to the Moon, Mars, or wherever. The payload is a very small percentage of the rocket that actually takes off, and if the launchers were properly designed, most of their major components could be recovered for re-use, as some private companies such as Space-X are trying to achieve. When that becomes the norm, rather than simply letting the launchers sink into the sea as NASA tends to do, space launches will be much cheaper and more efficient, because the only real cost would be the fuel needed.
There are some very worthwhile reasons to develop the technology required to land space craft on comets and asteroids, and it could at some point become a matter of life or death for everyone on Earth. There are an unknown number of asteroids orbiting the sun on orbits that sometimes bring them dangerously close to Earth, and these NEAs, or Near Earth Asteroids, are being carefully watched. As they are discovered, their orbits are calculated, and future orbits can then be predicted, which is where the 'landing on comets and asteroids' technology becomes important.
Without that technology, if astronomers discovered a new NEA tomorrow, and calculated that it would hit Earth in a few years time, there would be absolutely nothing we could do to prevent a catastrophe. Like the dinosaurs, we would have to sit and take the hit, and hope we survived, or that at least enough humans could survive to eventually rebuild the human race. An asteroid a mile or two in diameter would cause an almost unimaginable amount of damage to the Earth, its oceans, and its atmosphere, and could even wipe out life entirely.
With the development of space exploration, we now have at least a chance to do something to protect ourselves against Near Earth Asteroids. I read a while ago that plans are being worked out to send a mission, probably manned, to any asteroid that is found to be on a collision course with Earth. Once the asteroid has been reached and landed on, it would be nudged onto a slightly different course, probably by detonating nuclear bombs at carefully calculated points on the asteroid. Only a very small change of orbit would be needed, perhaps only a degree or two, or maybe even less, because when the asteroid has covered a few million miles, that change of direction will have made a huge difference to its trajectory . In theory, it could even be possible to guide the NEA directly into the sun, so it would never be a problem again.
Rosetta was launched on March 2nd, 2004 by the European Space Agency, not NASA, and spent ten years travelling to Comet 67P, AKA Churyumov-Gerasimenko, which it reached in 2014, after passing by two asteroids en route. It sent down its Philae probe to land on the comet, but that was only partly successful, as it bounced on touchdown, and not all the expected data could be gathered. Rosetta remained in orbit around the comet for over two years, sending back photographs and other information as the comet made its closest approach to the sun and headed back out towards the far reaches of the Solar System. As it moved further and further away from the sun, Rosetta was reaching the point where it would be unable to gather enough solar energy to power all its systems, and the team controlling the mission decided to arrange a controlled impact on the comet, with all onboard systems programmed to shut down permanently when it touched down.
The reason the onboard systems were permanently switched off was to prevent Rosetta 'waking up' as the comet aproached the sun again in the future, and sending out spurious transmissions that might interfere with other deep space missions.
Rosetta finally ended its mission by crash landing on Comet Churyumov-Gerasimenko on September 30th, 2016, sending back photographs until a few seconds before the impact.