There's a bit more to the ballast than just limiting the current. Completing the circuit through the starter bi metal switch also stops the 'glow' inside, allowing the bimetal elements to cool down and shortly open again.
While this switch was closed the heaters on each end of the fluorescent tube got nice and hot but the tube did not fire as this requires a higher voltage.
Now, as the bimetal switch opens, the magnetic field stored in the choke collapses, producing a high back EMF (~600V) voltage spike. This fires the fluorescent tube, the circuit is complete again with the electrons flowing through the tube, and THEN the ballast acts as a current limiter.
Once the tube is lighted the voltage drop across it is less than that required to activate the bimetal 'glow' switch again, most of the mains voltage drop is across the ballast.
You can observe this by carefully watching as a fluorescent tube is turned on. First there is a purplish glow in the starter, then the ends of the tube get orange hot inside, then there is a 'click' as the switch opens and the tube fires.
If the fluorescent gas inside the tube gets exhausted the tube will try to fire but the electron stream is not strong enough to maintain the current and the tube flickers on and off as the starter continuously tries to fire it.
Eventually one of the heaters at the tube ends expires and the annoying flicker stops but this could go on for many days if nobody comes and replaces the tube
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If the starter is faulty there will be no flicker in the tube nor any glow from the starter.
Klaus