What do you think will be the benefits of deep space exploration? A better way to ask this question is if it is at important for us to seek any benefits for exploratory science.
I believe science must not be limited by an apparent lack of understanding of its benefits. Science must be studied for its own sake. If we agree that exploratory science must be carried out regardless of whether there is an apparent reward to humanity then our imagination will be the limit.
What do you imagine to be the rewards from deep space exploration? People must have complained a lot during the early days of space travel because the period coincided with social unrest in America and not least a foreign war. The benefits of space technology can only be limited by our imagination.
The first thing we will gain is knowledge of where we are in the Universe. We are going to get a better handle of science. We are ever going to be curious to know if we are alone in the Universe. If life evolved on Earth, surely it must have evolved differently if there is life anywhere. After all evolution is a response to location specific conditions.
If life is there in the outer space and if the its general form is similar to ours what does it say of the Universe? That essential conditions are uniform or that this form is the best that there can be? Even here on Earth we have variations. But one variation stands above all, the Human Race and its ability to create its own artificial environment and to control growth and development.
If ever we going to meet with some civilized society that has a different form from us then we must brace for some intergalactic cultural shock.