haven’t came upon a clear “this type of plane did not exist yet but woodworkers needed it, so it became a thing” kind of explanation
The following page on Joel Moskowitz's site Tools for Working Wood appears to give just the explanation you're looking for, National Priorities in Early Metal Planemaking. An excerpt:
The metal plane showed up in England in the late 1700's as a great plane for marquetry -- with the form we now now as a "mitre plane". Better-heeled woodworkers quickly discovered that these metal planes were ... not only great for marquetry, but also for planing difficult woods. The metal body was stable, didn't wear, and worked consistently well. The only issue was that mitre planes were uncomfortable to use, so throughout the early 19th century we see mitre planes with handles cobbled up into them. This trend culminated in the form of the panel plane above, which is actually constructed like a mitre plane but has a regular handle like a wooden panel plane.
This ties in with other things I've read over the years about the origin of such planes, the where and why. The specific use-cases usually mentioned — highly figured woods, marquetry — were of course not new to European woodworking, what had changed was the demand for both. With urbanisation and a rise in affluence increasing demand, it drove a need to produce this kind of work more efficiently. And going hand-in-hand with this, it saw the rise of a class of woodworker who could afford them1.
Additional information, also from Joel, is on this tantalisingly titled page, Robert Towell - Inventor of the Infill Panel Plane. The relevant paragraph:
His first metal planes were miter planes and were much like everyone else's miter planes. Then Towell started making rebate planes. I don't know if he was the inventor of that design, but sometime probably in the 1830s - 1840s, Towell realized that most people were using their miter planes like regular bench planes. Ergonomically miter planes sucked, as there was just no place to properly grab a miter plane and put power behind it. Towell made some of the first metal panel planes, including the one in these photos. The actual shape of his panel plane wasn't new - it existed in wood for over a century previously - but making it out of metal was an innovation.
I think many modern woodworkers will grok this at least on a gut level. While there were then, and still are, various ways to skin any particular cat when you have a tool that works well you do tend to try to find as many jobs as possible for it! Especially the case if you're a tool minimalist, a he who dies with the fewest tools wins kind of person :-)
1 In contrast to the majority of woodworking craftsmen for the preceding 100-150 years. Even by a generation or two previous to this, individual craftsmen were still not generally well-heeled..... many might even be considered impoverished — working hand-to-mouth or close to it — despite the quality of the work they could produce, and fast.
