The road from theoretical physics to engineering is a very long one, so it's very hard to predict exactly what this would buy us. Relativity, for instance, spent a long time with no concrete engineering benefit, but now it allows GPS to be much more accurate by adjusting for the time dilation on GPS satellite clocks. As we get closer and closer to the mysteries at the heart of the universe, I think it's safe to say that the engineering benefit will be both more arcane and more powerful.

A lot of discoveries do not have immediate uses and some might indeed never have any applications. But discoveries can spurn others in unexpected ways. The most famous example of course if the WWW which came out of CERN, a pure physics research institution. Cryptography is another example that has had a profound impact on information security. But the most compelling reason, at least to me, is we investigate because we can! That is just human nature.

Basic research is the foundation of all engineering. You can't design things without understanding how the universe works. If you need examples, look no further than to particle physics, which has had a huge influence on medical imagery since at least the fluoroscope.

It doesn't buy you anything, just as fine art and music do not buy you anything.