Interesting question and comments. A few things strike me. First, a lot depends on the type of cabinets. Framed vs. frameless in particular. Both types have their merits, and I am not going to get into that debate, but most frameless cabinets I have seen on the market today rely on the wall to some extent for their strength and stability. In both cases, a floor that is not level or has waves in it can cause a cabinet to rack, drawers to malfunction or joints to separate when weight is placed on the cabinets. Maybe this is not necessarily a heavy countertop, but someone sitting on the countertop. As far as I know, all cabinet manufacturers recommend shimming the base cabinets at the floor to prevent this. In my experience it is extremely rare to find a perfectly level floor or wall. (and by extremely rare, I mean I believe it is possible, but have never personally seen it.) If the cabinets are not shimmed and secured to the wall, there is nothing to prevent the cabinet & shim system at the wall or floor from moving around.
The second issue that strikes me was partially mentioned before and that is door and drawer front alignment. In both frameless and framed applications, the cabinets are typically clamped and screwed to each other where 2 cabinets meet. This is to align the face of the cabinets and eliminate gaps. Then the drawer fronts and doors can not only be squared to the cabinet, but aligned with each other. If the cabinets are not secured to the wall for stability, any movement of a cabinet runs the risk of cracking the material around those connections.
Third, if the cabinets are not secured, finishing with any trim will be nearly pointless. If you want to run a piece of scribe to hide the gaps where the cabinet meets the wall or quarter round at the base, those would have to be connected exclusively to the cabinet and will likely not survive without being removed if the trim spans over more than one cabinet.
One final thought, I think the idea of free floating cabinets would technically work without running the risk of damaging the cabinets if the cabinets are of very high quality. Perhaps the type with feet as opposed to a continuous baseboard would do better. However, you would be taking an expensive cabinet and giving it he feel of a cheap installation. In my experience, I have seen a skilled installer who cares about the craftsmanship of his work take a set of the cheapest production cabinets you ever wanted to see and make them look like they belong in a million dollar show home. Unfortunately, I have seen a lousy installer butcher the installation of some very nice cabinets to the point where they were ripped out and re-done by someone else (rightfully so).
Whatever you do, I wish you success in your project!