You're looking for an argument against Coticules? Fine... There's no one Coticule that fits every job. Your argument about them having a fairly large cutting range on slurry, and being able to tackle a variety of steels is typically sound, but there's nuance about these stones that sort of tears apart the 'ultimate stone' argument.
It's easiest to see, if I just describe a couple of the stones I have...
I've got a super-hard La Verte, that probably peaks somewhere around 15K on plain water, and on a thick slurry can erase 600-grit scratches. It's a beast. At the same time, every time I sharpen a razor on it, I end up looking like Edward Scissor Hands. When I sharpen kitchen knives on it, I end up with a smoother edge than I like unless it's for something I'm slicing fish with it, or a sharpening a garnish-parer. EDC, again, it's lacking tooth... The thing's perfect on woodworking tools. Never seen a better, longer-lasting chisel or plane-blade edge on O1 or A2 than off of this stone.
I've got a particularly crazy La Dressante sample, out of several... Maybe peaks out at 8K-ish, and can lift from a Shapton Glass 500 on a dense slurry. The thing cuts high-carbide steels like crazy even on plain water (It'll eat HAP-40/CPM-M4! Not as keen as diamond, but it'll cut it faster than a 4K Shapton Glass HR stone on plain water, and leave a better edge.), and wears very little. It'll tear up a razor; it's like shaving with a hacksaw blade. At the same time, it's a great edge on certain steels for cullinary work. Major tooth, yet super keen. Not all La Dressante's behave this way. This is just how this one copy seems to behave.
I've got a couple La Gris; the common ones... One's just a total dud. Leaves deep random scratches, is slow, leaves a smooth edge in maybe the 6-8k range that's sort of good for nothing, is soft/wears fast, etc... Bad stone. The others aren't that bad, but lack a little something.
I've got a Les Latneuses, that creates one of my favorite straight-razor edges. Smooth, yet super sharp. It's a fast cutter with a high abrasive volume, but very fine and consistent particle size. Sucks on kitchen knives and most EDC, as it lacks some tooth, and wears a bit fast for woodworking tools, but for certain straight razors it's just amazing. There's a lot of variability amongst different Les Lat's.
Some Coti's can lift from like a 500-600 grit stone, and others struggle to start from a 2-3K stone on a thick slurry. Some create good edges for razors, others for woodworking tools (I've sharpened carving axes and knives, and chisels and plane blades on them.) , and others for cullinary knives, or 'Gentleman Carry' style EDC.
Sometimes other natural stones, like Arkansas or J-Nats will deliver a better edge on certain steels. Sometimes, a synthetic stone, diamond plate, a pasted strop, etc, will delivery the most amazing edge you've ever felt on that blade.
The key downside to Coti's, is simply the variability you get with any sharpening stone; particularly natural ones... There's no 'Swiss Army Knife' stone, for every steel/tool, as it's easy to imagine that Coti's are.
If you had a specific tool, that fit a specific Coti, you could conceivably maintain it on just that stone. Good Coti's do have a remarkable range. As you can probably see, though, no single Coticule is universal. Each sample is pretty unique.
Hope this helps...
