... but educational. Usually, INTs are taught as being connected (and on devboards are connected) to pushbuttons.

This is not the case. Pushbuttons are indeed very bad examples of external interrupt sources (also, except very specific cases (such as sleep mode wakeup or emergency input), pushbuttons are better served NOT by interrupts but by other means, e.g. periodic polls). There are microcontrollers (also '51 derivatives) with dedicated pushbutton (a.k.a. "keyboard") inputs, which do throw interrupts; but they are of a different construction and working logic than the conventional external interrupts.

As Christoph pointed out, interrupt input is intended to be connected to a device (or IC), which requests some action - e.g. and external UART signals that it has received a character. As soon as this request is processed - e.g. character read from the external UART - the external device releases the line pulling the interrupt.

Level-triggered interrupts are a solution for sharing a single interrupt input of the mcu by multiple such devices (using open-collector outputs of the interrupt signal wired-or together; or sometimes using a regular logic AND gate), where edge-triggered interrupts might lead to loss of interrupt if happen asynchronously and in any mutual timing (which is the usual case).

JW