What's the strongest, simplest woodworking joint, where you cannot pull things apart until you destroy the material- a dovetail. That's the reason why Schluter uses that shape on their uncoupling membrane. Relying on fibers that can and are designed to tear or break loose is relying on their ultimate strength and attach the tile to the membrane with more bond strength rather than mechanical strength. How thick is the thinset layer anyways? On most uncoupling membranes, the thickness is only used as pillars to the substrate to hold the tile up, not to anchor it to the floor in a lift-off manner.
Hopefully, now that people have an idea of what an uncoupling membrane is and how it works, they can then decide whether they should be using one in their situation, and then choose which one meets their particular needs and performance requirements. There's more than one out there. They do not all perform equally. They have different features you may or may not need (such as whether they can be used also as a waterproofing layer, for example). If you can accept that porcelain and glass tile have survived for centuries before modified thinset was invented because they set those tile over an uncoupling layer, you'd understand that a modified in this situation is not required, and because the membranes tend to be waterproof (not all are), that can pose problems with modified thinsets which need to dry to attain their maximum strength and stability. You'd also know that the tile is NOT bonded to the floor via a thinset mortar bond...the whole idea of an uncoupling layer to so PREVENT that bond, so the two can move independently. The goal is twofold: lock the tile to the top of the membrane so it doesn't come off, and two, provide support to the substrate so the tile won't crack because of deflection. If your subfloor is up to specs, and you install it properly, an uncoupling membrane will provide a MUCH more reliable installation under adverse conditions than any cbu or direct bond situation where you may need a modified to complete the job. And, it is easier to cut, carry, and install; plus, it will go on quicker than any cbu installation while providing the uncoupling function. Do you need it? Only you can decide. If you're paying labor, an uncoupling membrane is likely cheaper because it goes on so much quicker. And, if you add in the screws, and tape, and maybe you have to buy dedicated cutting tools to install cbu (say you're a DIY'er - a pro would already have them), the price difference is negligible. If you want to throw in a need for waterproofing (say you want to waterproof your laundry room, or extend the waterproofing beyond your shower into the bath), you need to be careful which product you choose.
My goal was to try to educate the readers on what they are, and how they work. Now, you choose which one will work best for you.