Several companies, over the years have attempted to produce modular effects in which a master controller could be used to coordinate them. In the case of the Korg unit, the master console simply provided regulated power, electronic switching and a space-efficient package. Others, such as the one that Sequential Circuits (Prophet 5, etc.) produced had programming of effects order as well. Vesta had a modular unit as well. These latter two were more like "frac-rack" units, where cards slid into a larger rack-mount chassis and common bus. Take a look at RG Keen's "FX-bus" article over at Geofex for an idea of a more basic version.
Ultimately, the advantages of these were the source of their problems. It was a case of in for a penny, in for a pound. Power was provided by the master console. Nice and regulated but you could only GET power to the module via the console. They all had their proprietary chassis and switching system, so if you bought one unit, you were essentially committed to buy a lot more, and there was no guarantee that you would *like* that company's take on that particular effect, or that anything made by anyone else would interface easily with the console. Take a look at any player's pedalboard, and what you will often see is a couple of Boss pedals or DOD pedals or MXR pedals, but rarely all pedals from the same company. Typically, with all the modular systems I've seen, wanting to use something outside of their unique offerings tended to instantly screw up all the advantages provided by the console. To my mind, this was why such units came and went.
The comparison between the Korg PME series (I have one module - the Waveshaper - that needs to be situated into another chassis to be used) and the Tone Core series is a little off, though. The Tone Cores do have a modular element (and look for interesting developments on that front), but are designed to be standalone units. I'm sure they'd love for everyone to buy all of them, but buying one doesn't leave you out in the cold the way it did with the Korg series and related modular systems.