Note that the relatively small "filament transformers" with 6.3 V secondary are rated to deliver 6.3 V at a specified current.
At currents below that, the voltage can be substantially higher, which can shorten the life of a 6.3 V heater in a vacuum tube.
Also, a lot of vintage equipment was designed for US operation at 110 VAC, but the modern specification is 120 VAC (having evolved through 115 V and 117 V), so the heater voltage may be 10% higher than intended.
This is a complicated question. One useful reference is R B Tomer "Getting the Most Out of Vacuum Tubes", H W Sams 1960, reprinted by Audio Amateur Press 2000.
That reference does not discuss DC heating in detail, but does mention the connection of input tubes' heaters to the output tubes' cathodes in audio amplifiers to reduce hum with DC heating, since the 12AX7-type tubes are run at plate current far below saturated cathode emission, so a low cathode temperature is not harmful.
In my recent builds with 7586 Nuvistors, I wired three heaters in series (nominal 18.9 V at 0.135 A) with an additional 39 ohm resistor, to work with a 7824 voltage regulator. This has the advantage of greatly reducing the surge current on turn-on with cold heaters. (I used such a network with each of the three-triode amplifier stages.)