To name a few problems:
You need enough bandwidth to faithfully reproduce the signal on the receiving end, including preventing edge jitter/phase distortion.
Many protocols have multiple digital channels. DVI starts out at a minimum of 4 channels, if you count each differential pair (red, green, blue, clock) as one digital channel and ignore the DDC channel used by the monitor to signal which resolutions it can handle.
Some protocols, notably USB, is using a bi-directional differential pair. Without being aware of the protocol, you can't know whether the host is currently transmitting or receiving over this channel.
You need to deal with interference. Without being aware of the protocol, it would be very difficult to reproduce any data lost, since you don't know where a packet starts or ends, etc. With knowledge of the protocol, the KVM can for example acknowledge that a USB packet was received, one side, and the transmitting side at the time could resend it if no ack comes back as expected. Likewise, the KVM could repeat the previous display frame if it detects interference, instead of showing a blank screen or whatever noise it picks up as interference.
Likewise, you need to deal with not creating interference. The unlicensed bands are very crowded with things like wi-fi and bluetooth, and you need to keep within the legal transmission power limit. You could ignore that and wait until your neighbors come knocking on your door wondering why their wi-fi stopped working all of a sudden.