Yes, they are “rarely” observed on human life timescales. It was estimated that approximately 50 genes evolved pr. 1 million years in rice plants. That’s one gene every 20.000 years on average. No wonder we only see it rarely, nobody lives that long. We’ve only had the technolog to look for them for a few decades now.
But there are actual experiments where it has been shown that non-coding DNA can yield functional benefical protein coding genes. The papers on those have been linked, and you continue to completely ignore them.