What would it take to make a PS/2 keyboard interface hot-swap?
Somehow, un-plugging or plugging in a keyboard can cause a surge. I don't recall having these issues with serial ports (RS-232, Appletalk, etc), parallel ports, VGA, etc.

These don't power the equipment on the other end.

What would have to change to make a PS/2 keyboard interface capable of hot-swap?

There has to be a way to limit current to prevent a faulty device from shorting the power supply and frying the motherboard or simply crashing the PC due to a shorted +5V rail. Even if the device is not faulty, if it has a big enough capacitor, connecting it could cause inrush current and a dip on the +5V rail which could cause a crash.
A fuse is a crude way to do this.
USB was designed as hotplug, so it uses active current limiting. There is a whole family of chips to handle this. Here is an example.

Texas Instruments TPS2001D USB Power Distribution Switch is intended for applications where heavy capacitive loads and short circuits are likely to be encountered, such as USB. The TPS2001D limits the output current to a safe level by operating in a constant-current mode when the output load exceeds the current limit threshold. This feature provides a predictable fault current under all conditions. The fast overload response time eases the burden on the main 5V supply to provide regulated power when the output is shorted.

It also provides a FAULT signal to the computer so it knows what's happening.
To make PS/2 hotplug, that wouldn't be enough though.
You'd need a connector that makes contacts in a specific order: ground, then power, then signals. USB does this by making the pins that should make contact first longer. Without this type of connector, power and/or signal can make contact before ground, which means the device will receive IO signals before it has power, ESD protection diodes in the device and/or host will conduct current and it will power itself through its digital IOs, which can lead to fried ESD diodes, or worse latch-up. This requires special mitigation measures.
Also, you'd need the software in the PC to handle hotplug and register that a device has been plugged. With USB this is easy, the chipset does it automatically and raises an interrupt when a device is detected.
EDIT: Also an important part of the USB connector is the shield makes contact first, so any ESD event happens between shields and signal pins are not involved. This is probably the case with PS2 too, since the shield protrudes quite a bit.
The absolute worst case hotplug connectors are RCA audio (signal connects before ground), and of course the audio Jack (signal connects first AND all pins short together during insertion).