Why use aluminum wire in an (old) TV degaussing harness
In consumer electronics there is only one reason.
Price
Saving 10c on a run of 100,000 devices saves $10,000
the degausing coil doesn't need to be compact or have to low skin-effect losses so there's no compelling reason not to use aluminium.
Reasons for using aluminium wire in a CRT degaussing harness:
The lower electrical conductivity of aluminium (only 63% that of copper) would be good enough for the degaussing application.
The lower density of aluminium (only 30% that of copper) would make the harness lighter and easy to handle.
The lower weight combined with the lower cost of aluminium wire (only 40% that of copper) would result in a cost saving of 88%.
The cost saving would be considerable even should the wire gauge be increased for increased rigidity.