Even from domestic standpoint it is a bad idea to replace just the starter and not the lamp. Because it is always the lamp, what is failing first, even when it initially may not appear that way. What happens is the lamp electrodes get depleted, first consequence is prolonged reignition delay, causing the starter to constantly glow and heat up. Initially just not enough to close its contacts, but still enough to clean out its electrodes so making its component (the EME suppression capacitor, the plastic case,...) degrade and the threshold voltage to go down. Only then the heat starts to be enough for the contacts to close, so start the EOL flashing. The fresh starter may still have its trigger voltage a bit higher, so it will again just glow and warm up not enough to close. But still degrade as well, so start flashing again very soon, so ruining a new starter.
Now if you replace just the lamp (and not the starter), the old starter, being exposed for quite a lot of overheating by the failing lamp, developed shifts in characteristics due to material fatigue, so wont preheat the new lamp properly, wearing it faster than a fresh starter would, leading to premature lamp failure.
The thermal cutout starters benefit from the fact the cut out device disconnects them immediately once they start to heat up, so wont let them to be exposed to the heat for that long time, so allow them to operate well over multiple lamps (usual rating is 3 lamps). The thing is, the starter starts to suffer practically only once the lamp starts failing. Normally the starter get shot by the first failing lamp, with the cutout makes it survive two lamp failures, so operate the thrid lamp over its life.
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