But back in the day of the Apple II, I'm assuming that it was easier to solve the key-repeat problem with hard electronics than it was with the operating system or application.
Does anyone know if this is the case, and if so, the specifics?
I realize now that while the answer to your question was part of my earlier post, this wasn't clear.
Basically, the key repeat problem was solved with a separate key on the Model 33 Teletype, which had a mechanical keyboard. Since this was what people were used to, straight ASCII video terminals, which were designed to be connected to any minicomputer that used ASCII, followed this practice.
Meanwhile, IBM made electric typewriters. On those, it made sense for a few characters, such as the underscore and the period, to automatically repeat. This was done when the key was pressed down somewhat further than done for normal typing.
So, when IBM made its 3270 terminal system, while it didn't use special double-action switches, having keys repeat when held down long enough followed what people were familiar with from IBM typewriters - and the IBM 2741 terminal, which was based on a Selectric typewriter.
The 3270 transmitted characters to the host computer, not key up and key down codes - in fact, it even lightened the burden on the mainframe by usually operating in block mode. That's why the "enter" key was down where the right-hand Control key is on a Model M; it was meant to send a screenful of data, not to be used for every line, so a more awkward position for less frequent use seemed reasonable.
The original PC keyboard was derived from the one on the IBM 5251 display station, so, although the IBM PC used ASCII for its character set, the keyboard was the product of a line of evolution of keyboards on EBCDIC terminals, and those in its line of descent did not have repeat keys at any point.