Over the course of your natural lifetime, your past light-cone will extend by about 100 years. Since it already envelopes almost 14 billion years, you won't get much new information relative to what you already know.

You are forgetting the impact of improving science. In fact, most of what we know about the 14 billion year light cone has been added to our knowledge in the last few hundred years due to improved instruments and improved theories. As theories improve, we build better instruments and reinterpret data we collected earlier. As I explained in a recent comment, suggesting new tests for distinguishing between states of the universe is an important part of the progress of science.

You are right about the growth rate of the accessible light cone, but we will continue to improve the amount of information we extract from it over time until our models are perfect.