Significance of Law of reciprocal proportions
The comments certainly clarify the law of reciprocal proportions and are an excellent tutorial on how to write a good question but sheds little light on your question “Is there any intuition/specific reason that Jeremias Richter came up with it?”
From reading a number of short bibliographic sketches about Richter it appears his primary interest was mathematics.  The title of his doctoral thesis was, roughly translated, The use of Mathematics in Chemistry  [https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/richter-jeremias-benjamin].  His study of quantitative relationships in the neutralization of acids by bases lead to the law of equivalents. [https://encyclopedia2.thefreedictionary.com/Jeremias+Benjamin+Richter ]
Based on these and similar biographical notes one might argue that he arrived at the law of reciprocal proportions not through “intuition” at all but rather through an empirically based and numbers driven approach.  When a mathematician sees a pattern or consistency in “the numbers” they then might be seek to understand the natural forces giving rise to their observations.
A modern and well written example of “math driving science” can be found here. https://www.quantamagazine.org/geometry-reveals-how-the-world-is-assembled-from-cubes-20201119/ “Scientists Uncover the Universal Geometry of Geology”