(Though, that keyboard and mouse were different ports was stupid, so it loses points there)
I can totally see how they were designed to theoretically allow for it; practically, the tactile feedback for the correct orientation is just way too subtle.
And regarding the two different ports: I can't remember (or rather, I was never motivated to revisit the plugs once connected to experiment, since it was such a pain) – was there a technical reason for that, or could modern mainboards/BIOSes/OSes detect and correct for that?
IIRC, there was a technical reason in that original mainboards lacked the circuitry to detect and correct for it (I think different mouse vs keyboard interrupts were involved?), and it would have been a extra x¢ on the BOM. But modern mainboards just use two of the same circuit and in fact do work fine if you swap them (tested just now, sample size of 1).
The only upside of PS/2 was a higher mouse data rate, particularly with high monitor refresh rates, made mouse movement smoother. You didn't get this for free in Windows though, you needed a registry tweak to tell the mouse driver to bump the sample rate.
The huge downside was that PS/2 peripherals couldn't be inserted when the PC is turned on. They need to be inserted at boot time, and aren't detected if they're plugged in later.
And the keyboard and mouse connectors were physically the same but not generally switchable.
That sounds silly, but I forgot a non-trivial number of times.