I'm left wondering what exactly was the *real* problem that PAL
was intended to fix. It appears that the NTSC tint control could
only address a fixed phase offset between the colour burst and
the subcarrier, with both transmitters and TV sets able to
maintain that offset sufficiently closely that the hue wouldn't
vary from left to right of the picture.

Correct.


Other issues, such as non-linear phase shift would have been
a problem for NTSC viewers, regardless of the tint control.

Also correct.


So were NTSC viewers tolerating colour pictures that couldn't
be set right even with the tint control? Or is there something
else that I've missed?

You /have/ missed something, which I explained "long ago and far away".
grin

The US TV-distribution system DID NOT generally suffer from non-linear
group-delay problems, whereas the European system DID. That's it.

Even without the extra delay line, there is some degree of visual color
averaging, which tends to mitigate the phase error.