'Inrush current' isn't be a serious problem for filaments until they get degraded with use. All lamp filaments lose material at the high temperatures of service- it migrates off the filament as metal or carbon vapor and can often be seen on an old bulb near the base, where the glass is coolest. Inert Gas filling reduces the migration of material, [as does use of a thicker wire of course]. 'Vacuum' bulbs are obsolete simply because gas filled ones last longer.
The 'inrush' "problem" is supposed to be worse with metal filaments, as resistance increases with temperature = high amps at start. The speed of the temperature rise in a modern bulb is such that this resistive effect is of little consequence, and there is negligable temperature overshoot. Failure may also be due to minute dislocations or faults growing in the filament material with each cycle of on/off, a function of material quality,
[ie 'They last longer if you leave them on'].
Tungstan wire is drawn from powder-metallurgy formed slugs- the material is never melted, so the wire is a 'welded' material. Carbon filaments were grown by a plant and so suffer from biological variability. Interestingly, carbon filaments had a negative resistance curve, the resistance
falling with temperature rise. They still failed eventually - often by blacking out the glass surface with so much soot that the light couldn't get out!
The '100 year' carbon bulb is running at a very low filament temperature. This has slowed migration to a negligable level, but eventually.....
Alan