There are some details where the carbon performs better, with the main task of being an efficient and long lasting incandescent radiation source it severely lags behind its metal filament based counterparts.
The carbon evaporates way faster than tungsten, so as an incandescent lamp does not allow any high efficacy at all. For the heaters, to get reasonable life it would have to be operated on so low temperature, you need way greater surface to radiate any usable power. So for that the metal filament ceramic rods are way better and are capable to operate directly on free air...
So I don't think there is much applications for the electrically heated carbon filament.

Carbon filaments are odd. They CAN be lit at low temperatures (a very dim, reddish glow) in open air without quickly burning through, unlike tungsten. I did this with an old NALCO 32cp carbon filament lamp that had long lost vacuum due to a crack in the stem. There was build up of snow-flake like deposits on the inner glass envelope. I lit this on a dimmer, it stayed lit when the filament just started to glow. I cranked up the dimmer, and the filament suddenly went white bright in two places and burned through.

Carbon filaments are odd. They CAN be lit at low temperatures (a very dim, reddish glow) in open air without quickly burning through, unlike tungsten.

This is not that much about the temperature where it starts to react with oxygen or so, but about the thermal stability along the filament (in other words about the tendency to form hot spots vs equalize the temperature along the filament).
With a long and thin filament structure heated by a passing current, the highers power dissipation concentrates on spots with the highest resistance (the current is the same along the whole filament, so the local powerr density then depends on the local voltage drop).
Because carbon has a negative temperature coefficient, the highest resistance will be on the coldest places. That means the heat focuses on the coldest places of the filament and when they warm up, it moves elsewhere (well, if the current does not changes).
With the positive temperature coefficient of the tungsten (and many other metals), the spot with the highest resistance is the hottest one, so the heat tends to concentrate there. That means any non-uniformity in the filament and one spot becomes way hotter and it will be that one, which will then receive most of the power.
So although the carbon filament as a whole is way less stable than the tungsten, its tendency to equalize the temperature along it's length allows you to manually adjust the power so, it glows steadily and yet do not reach the combustion temperature. On the other hand with the tungsten, it is the hot spot formation, which makes it to very quickly exceed the ignition temperature and so causes the filament to burn.
Normally when the thing is intended to operate as an incandescent lamp, majority of the heat dissipation goes via radiation and that goes with the very steep T^4 function, so stabilizes both local temperatures of the tungsten, as well as overall temperature of the carbon. But on free air and way lower temperatures the radiation part is way weaker than the convection, which is governed by way less steep function.

By the way the tendency to hot spot formation of the materials with positive TC and the overall thermal instability of the materials with a negative Tc is the main reason, why the rather low temperature incandescent heaters operating on free air use an alloy (beside it's high temperature robustness on the free air) with very low TC for the heater (= filament) wire.

Then why the filament appear uniformly hot in dimmed Incandescents, even in worn ones where it can be seen that it is not so uniform when visually inspected (on a cold lamp) ?

Then why the filament appear uniformly hot in dimmed Incandescents, even in worn ones where it can be seen that it is not so uniform when visually inspected (on a cold lamp) ?

Normally the incandescent gas fill is designed to conduct as little heat as possible. So the dominant cooling mode remains still the radiation. It is the steep dependency of the power on the temperature (at temperatures where it glows visibly), what keeps the temperature rather even when the power density varies along the filament.
But because air has way lighter molecules and they are not just atoms, it carries the heat way easier. So when just the air is round the filament, the convection heat loss is way stronger, so the radiation stabilization mechanism may not be sufficient to prevent the local runaways.

Is it possible to dim an ordinary GLS lamp (one that made many hours allready) to a point where the no uniformity (as result of filament non uniformity, not result of heat sinking by the supports) become visible by naked eye ?

Is it possible to dim an ordinary GLS lamp (one that made many hours allready) to a point where the no uniformity (as result of filament non uniformity, not result of heat sinking by the supports) become visible by naked eye ?

With some lamps you may observe some sections to glow earlier than others, but with many lamps the critical temperature (where the radiation becomes so strong it makes the temperature equal) is just too low.

Even in the air the heating may be with some lamps so even, you will be able to warm it to visible glow still without runaways. It really depends on the exact filament shape, it's state (degree of nonuniformity),...

With the air it is just more likely to be thermally unstable than with Argon (or even Krypton or Xenon) fills.