A research paper should deliver novelty, so I wouldn't expect research papers that advance understanding of an existing topic, without providing novel material. By comparison, a review paper or a handbook chapter might achieve such an objective. For instance, Very Short Introductions. Some review papers are highly cited, so presumably they are considered valuable.
EDIT. To conclude, research papers advance knowledge, whereas review papers, handbook chapters, etc. advance our understanding of existing knowledge. Thus, by my reasoning, "research papers which are written on understanding" aren't common, but review papers, handbook chapters, etc. "on understanding" are common.
EDIT II. The scope of the question has changed since I provided this answer. I agree that research papers providing new proofs of known results most certainly exist. My answer acknowledges the existence of such papers, because they deliver novelty.