You're mixing up two related concepts.

Software support for hotplug can be added or removed as desired. That's an OS feature. You could absolutely reconfigure the interrupts without rebooting, if you felt like it. But hot-plug support starts in hardware, as an attribute of the connector. Being able to safely make and break connections while the circuits are electrically "hot", without damaging the circuitry on either side.

Generally, this can be done two ways:

The first is by having circuitry that moves so little power, or moves it in such a way, that it can't be damaged by the connections being made or broken in random order. For example, plugging a light into an outlet. It doesn't matter if the line or neutral conductor makes contact first, since the light either receives power or it doesn't, and neither state is unsafe. (Don't touch the blades of the connector. That's another matter entirely.)

The second is by having a connector design where some circuits are guaranteed to be connected before others. This is typically called a "make first / break last" scheme. At its simplest, the metal shell of a D-sub connector is really really likely to make contact before any of the pins, and in practice is effectively a make-first. But all the other pins make contact in random order. Compare to something like the SATA power connector, where the grounds are longest, power pre-charge after that, and main power at the very end. This is unconditionally safe to plug and unplug while hot.

VGA is hotplug-safe in practice because while the connector isn't really designed for it, as long as ground makes first, the analog video signals aren't picky at all (they're capacitively coupled and have no DC component), and the DDC data lines have enough short-circuit protection to tolerate whatever. (Because the D-sub connector also isn't "scoop-proof" -- it's possible to touch the male pins with the shell of another connector during clumsy mating, all circuits have to tolerate shorts to ground.)

RS-232 by the way, which was designed for D-sub connectors, contains language in the spec requiring that all circuits be tolerant of indefinite shorts to any other pin or to ground. It doesn't have to function in that state, but it's not allowed to sustain damage.

PS/2 isn't hot-plug safe even if you preassigned the interrupt (or booted the machine with the keyboard connected and then unplugged and replugged it later), because the pins aren't sequenced, and the circuits aren't designed to tolerate random mating order. If the power and data lines connect before the ground, you can get a CMOS latchup situation in the controller silicon that can only be cleared by total power removal. In practice this was fairly rare because the ground usually made first, and before I understood about this, I only smoked 2 motherboards' PS/2 ports despite hundreds of hot-plugs of keyboards and mice.

The canonical example of a terrifyingly-hotplug-unsafe connector is the TRS phone plug and jack. They change order during the mating process. Some old guitar effects pedals used this connector for power, and you were virtually guaranteed to smoke a transistor if you hotplugged it. These connectors were meant for telephone signals (which can tolerate polarity reversal and indefinite shorts to ground, by design), and some idiot decided to put power over them.

Note that there are no drivers or interrupts being assigned to a guitar pedal. Software support is entirely unrelated to the electromechanical phenomenon of hot plugging.