Besides satisfying our human need to explore and discover, these missions bring about a great deal of technological advancement.
Wireless digital communications, for one, has benefited tremendously from the advancements in modulation and coding theory that were motivated by these deep space missions, and those technologies helped bring us where we are today with the mobile communications we all take for granted.
It is quite remarkable that at the time of their launches, Forward Error Correction (FEC) decoder hardware did not yet exist for the codes that were used and in some cases still being used to receive data from these distant explorers.
One of the comments asks why it's important to have deep space missions at all? The question is fair, and in the context, the commenter notes that the resource (high-tech) labor can be placed elsewhere. Some answers: deep space missions produce a disproportionate amount of scientific information when compared to their cost, which is trifling compared to manned spaceflight. That's the ROI: you get a lot of knowledge for little. As for other uses of engineering time, well, the earth is already self-sustaining. When we run out of something, we'll find an alternate, or do without. As for all the social progress we'll garner, well, note well: life is a competition, and all of the feel-good effort in the universe won't make it otherwise. "The poor will always be with us." That means not only economic poor, but poor in spirit.
On the contrary, why is it so important to have deep space missions at all? I see countries racing to put man on moon again, send missions to mars et al. Whats the ROI on such investments? Scientists and Engineers time is much more well spent figuring out ways to a greener/self sustaining planet earth and to industrialize across nations, which can in turn reduce economic disparity and elevate the living standards of earthlings in general. Space is just fantasy!!
Humans explored the world in past centuries on missions that took years with high costs and uncertain paybacks. It took decades or centuries to realize the value of what was discovered, the people that funded the first missions and spent their lives in doing so only had their vision to keep them going.
I think the mission lifetime and data rate issues are important, but can be overcome; in the process these areas have their own developmental value. There are many disciplines that will gain from more sophisticated expert systems that can capture institutional knowledge and retain it for multiple lifetimes. Meanwhile low data rate and long cycle time loops are not new to engineers and further development in distributed/local intelligence and redundant systems can mitigate these issues. Finally, the nature of the mission will appeal to a smaller population of engineers, but there will always be a few willing to be motivated by this kind of grand vision and intellectual challenge.
The engineering issues in building devices that work for so long in such hostile environments are significant. The patience and stamina for deep-space missions, however, also require ongoing human support. Getting into orbit and getting to the moon involved travel that was well within the life span of the astronauts and provided new images and insights to the eagerly waiting global citizens. The incremental knowledge gained in these new extremely long missions is much less flashy and comes much slower so the general population is much less supportive.
The exploration is still important and worthwhile. We never know what we will discover in outer space - but the insights gained in engineering such missions may also have unexpected benefits in addressing such issues as working in the depths of the ocean to seal leaking oil wells.