OSC is not related to MIDI in any way, it is not simply MIDI over network at all, they bear no relation to one another other than the initial idea behind OSC was also for controlling synthesizers and music things. But its use has ballooned far beyond that.
OSC is a network data transfer specification for sending data packets with an address structure similar to a web address, making it very simple to configure and understand.
So as an example, Qlab is a software I use a lot. To tell Qlab to fire a particular cue you might use an OSC message such as:
/workspace/Hamlet/cue/16/go - this will fire cue number 16 in the workspace for Hamlet (if you had more than one workspace open), and also advance the playhead.
It supports wildcards in the address string, so I could send /cue/preshow*/active 0. this would deactivate any cue with "preshow" as a prefix in its cue number.
It also supports copying details from other cues places, in the case of Qlab I can send a message that uses the details from another cue, so /cue/16/levels/#cue/9 0 0#/ 0 0
This will copy the fader level for the master fader from cue 9 into cue 16.
These are specific examples for one piece of software, but as you can see it is nothing like MIDI at all. It can operate over UDP (often more common) and TCP, which allows for data feedback. Often feedback from requests is formatted as json strings meaning it is relatively straight forward to parse. And it also supports sending bundled packets of messages, so if there are many messages that are time sensitive so they all need to trigger at once then they can be sent as a bundle instead of a string of separate messages. Whereas MIDI is a strictly serial protocol, and extremely slow, low resolution, has very limited number of things it can control (16 channels) OSC has none of this limitations. With it's flexible address structure that can be defined on the fly it can access hundreds of thousands of potential parameters at once, and update the list as it goes.
Now I don't think that KM would need to support all those features, but to be able to send UDP OSC data messages that could be constructed using variables etc at the very minimum would be a great feature.
It may have been proposed as an alternative to MIDI, but that is where the connection between them ends.
Here is some further info on the protocol: