Let me take the first stab at this one.
My experience relates to work and association with two family shops (one-print and one-typeshop) over a span of thirty years.
Yes, asbestos was inside those metal pots, however the asbestos was completely enclosed with the exception of a small quantity around the mouthpiece. That exposed asbestos is not loose, but is cemented and further covered by a sheet metal plate.
From time to time the asbestos was repacked, but frankly this practice varied from shop to shop. In our practice, pots were never routinely repacked except when a metal heating element was exchanged (once or twice to my recollection). Thus, in my experience the asbestos rarely had an opportunity to escape and become airborne.
Lets put things into perspective; during the 70's in the US (and likely in Europe and Australia) asbestos was put into ceilling tile, floor tile, spackling compound, wallboard, blow dryers, heaters, insulation, etc, etc, etc. There were far more extensive areas of exposure to asbestos to an operator than from a fully enclosed heating apparatus. Three important exceptions: in gas flue systems, sometimes people would liberally cover the vent stacks with cemented or rolled asbestos.

Another exception is if an operator/ machinist routinely worked on numerous machines' heating elements alot without respiration/occupational protection. Finally, what about the remelt furnaces? Sometimes these remelt furnace were thrown-together affairs and the favored insulator was dry-cemented asbestos. Nasty stuff if it gets loose and on a hodge-podge remelt furnace there may be alot of it.
Apart from linotypes, how about asbestos insulation on thermograph heaters and the dry sprays of various kinds. Talcum powder on press tympans?
Thats my contribution.
Dan