Leaf blades appear when swords were still being made with bronze. Bronze swords were typically lightweight - often short, often thin, and often with weight-saving blade geometries (which, since these were cast, didn't need to be forged/cut). For good cutting, a thin blade is good. Some width is needed, for strength and also to have sufficient weight behind the blow (which doesn't mean a lot of weight, just enough weight).
However, bronze isn't as stiff as iron/steel - its elastic modulus (Young's modulus) is about half that of iron/steel. So, for a given thickness and width, a bronze blade bends more easily than an iron/steel blade. An easy solution is to make the blade thicker: thick = stiff. To avoid excess weight, make the thick part of the blade narrower.
Combine a thick narrow base of the blade (for stiffness) with a thin wide cutting portion (for good cutting), and you have a eaf-blade.
Historical leaf-blades are usually thin-tipped and light. They aren't heavy hackers/choppers. Rather than "forget about fast slashing attacks", they're all about fast slashing attacks. (19th century artillery gladii don't follow this pattern - they're made as brush-cutters, and IMO are poor fighting weapons.)
The basic idea of thick narrow base and thin wide cutting portion stayed in use. It largely disappeared from straight double-edged swords, but can still be seen in some falchions, in kukris, in niuweidao/oxtail dao, the British 1796LC sword, and others. In many of these swords, the wide portion of the blade is about 1mm thick - these swords aren't heavy choppers. (The kukri shows that this is relative, since the main cutting part isn't particularly thin, just much thinner than the base of the blade.)
The stiff base of the blade also makes them better for thrusting than a blade that's thin and wide all the way.
There are exceptions. Some bronze blades are only a little thinner at the wide portion than at the base. In these cases, the base is not particularly thick, and perhaps the idea of a thicker base for more stiffness for better thrusting wasn't felt necessary. Also in these cases, the weapon is still light, perhaps about 600g for a weapon of 24"/60cm total length. At these weights and lengths, the weapon is still agile even with a thickness of, e.g., 5mm at the widest point.