I remember old television sets tubes filaments glowed brightly when the tv was switched on. Then they shut off and after a few seconds went red glow (normal operation). This is the case in almost all televisions I have seen. I do not think they worried too much for the inrush current when the filaments are cold. And I have never seen a tube filament broken from that era.
I recently built up a hybrid valve/mosfet amplifier running of 12vdc.
I couldn't get it to play ball and someone suggested a higher dc voltage.
So I tried 30 volts only to suddenly realise the heaters were running off 30 volts too !
Luckily the heaters survived it. So it looks like heaters can take a bit of abuse.
There is something additional, that was explained to me *decades ago* by a tube engineer: the maximum filament to cathode breakdown voltage.
For instance the 12AX7 / ECC83 tube has only 180 volts peak rating, which very likely could be exceeded on a direct 230 volt line.
The 50C5 which was designed for the "All American Five" transformerless radios, has a slightly improved margin of 200 volts peak rating. But the line voltage is only 120 volts AC.