I have many times replaced starters on failed tubes, however in the main a couple of weeks latter it has failed again. The reason they fail is the tube has come to end of life, so needs repeated re-starts, so in real terms when a fluorescent fails it is better to replace tube and starter together on average although one may replace some good units, it saves that much labour well worth simply replacing the pair.
However the old fat 65W tube is no longer made, the 58W tube will fire up, but within 6 months it's failed again, and a fluorescent tube should last at least two years, swap the ballast to a 58W and then of course it will work OK, however to swap the ballast you need to remove the whole fitting to gain access to fixing screws, so may as well replace whole unit.
Today we use all HF ballasts, but back in the day of the 65W tube they were all wire wound, with the wire wound ballast 220, 230 and 240 volt rating was important. During the building of Sizewell 'B' power station we were using 110 volt fluorescent fittings, in fact these were 230 volt fittings with an auto transformer these auto transformers had three connections marked as 127 - 0 - 110 volt and as standard they had lamp connected to 237 volt and input to 110 volt. When I used a clamp on ammeter I found around 0.8 amp was used, swap to 127 volt and the amps dropped to 0.6 amp, this is a huge difference for just 17 volt, had it not been 110 volt there would have been no option to adjust voltage however at one time you could get devices which monitored the voltage and auto changed tapping on an auto transformer, today with HF ballasts they are no longer required.