I found several NOS Sentry 40 watt air thermal starters from the 1940s on ebay recently and the information on the box said that the thermal starters extend the life of the bulb.
I installed two of them in my 1941 Fleur-o-ray 40 watt Double Paracyl fixture.
This fixture has the original 1941 GE ballast with the starting compensator.
The two new GE 40 watt K&B bulbs started up rather quickly with out any blinking at all.
According to the 1942 GE fluorescent lighting manual, the air thermal starter keeps a small current in the bulb filaments during starting and operation extending the bulb life.
Some of the first GE 40 watt ballasts had the thermal starters in the ballast requiring the ballast to be replaced if the starter failed.
After many complaints about this, the now familiar replaceable twist in starter was designed.
The air thermal starter was used originally by GE early on before the glow bottle starter.
They do work really well, but they do have a down side and may be it is the reason the glow bottle type starters were more popular.
While they do work ok, if you shut the fixture off, and then turn back on, the bulbs won't start again for about 60 seconds or even longer sometimes as the starter has to cool down before resetting itself.
This does not bother me, but for some applications, it could be a problem.