Leg levelers greatest attribute is that you can get your Full Access cabinetry perfectly level, regardless of the floor and wall conditions (with Full Access cabinetry, it is imperative that your cabinets are level and plumb if you want your doors to operate and look proper, 3mm or 1/8" reveals are very unforgiving).
Another attribute that most appreciate is that the cabinets are fully supported on all four corners, not just at the front where they might be shimmed, and then dependent on the shear strength of the screws at the back. In the age of stone counter-tops, which are extraordinarily heavy, this is more important than it was even a few years ago.
While we are on the topic of heavy stone counter-tops, it's nice to know that the sockets that receive the legs are actually partially under the end panels, transferring the weight of the counter-tops to the floor rather then the cabinets joints.
Perhaps the greatest attribute of all is that if there is a water incident in the room where the cabinets are installed (pretty common in kitchens and baths), even if it is only a minor incident like a leaking ice maker, faucet or dishwasher, the cabinets will not be damaged. Only the toe kick will get wet, and it can either be removed to dry, or easily replaced.
Many people appreciate that the toe kick can be removed if there is ever a need to access the space under the cabinets. To have the ability to add or reroute plumbing pipes or electrical wires, or get at heat and air ducting can be a very useful thing, not to mention you just might want your bug man to be able to get at that space when you have the inevitable rodent issue.
From the manufacturing perspective, leg levelers allow us to get 6 base end panels out of a single sheet, where full height toe notched ends only yield 4 base end panels. This extra material yield translates to lower material cost, and thus lower cabinet cost than it would be otherwise.