My Amstrad CTM644 CRT 'monitor', makes a high pitched whine [...] My research indicates that this is just the scanning frequency of the tube,
The ~15 kHz line frequency is the most likely source. More exactly, it's the retrace, as that's not only one of the most powerful moves the ray does - which equates to higher currents used to initiate it - but it's also nicely regular, so is detectable by our ears. 15 kHz is at the upper end of what humans can hear - and usually only in our first 2-3 decades, as high pitch hearing is the first thing we lose.
and not a fault of the electronics.
Erm, no. It is usually a fault of the electronics, but not with its electronic operation, but the mechanical mounting/stiffness. The sound comes from coils that move (vibrate) due to the changing magnetic fields.
Did consumer CRTs always do this in the 80s, and I have forgotten? Or has my monitor got worse over time?
Both. Often coils and the like are pressed into place and/or glued down to stop them from making these noises. When not done properly, these sounds come even with new devices.
In addition, depending on the design of the coil and its mounting, it may be temperature sensitive, meaning the device has to be heated up to ensure a proper fit. That's why this sound often comes only during warm up. This was extremely common with early (1960s) TVs, but later as well.
The problem may get worse due ageing which adds shrinking and/or loosening of the mountings. Again, depending on the design and changes this may only be an issue during warm up.
Exact measures to remove this (if possible at all) depends much on the type of circuitry and its mechanical design. The best approach would be to simply drown it in glue... except that would most likely result in overheating :( So if you want to get rid of it, a lot of experimenting is ahead of you - mind the high voltage.