I think the 4CX250B (and many of its bretheren...the 4X150A/D, 4X250, 4CX300A, 4CX350A, etc.) are misunderstood. Further, I think that most of the misunderstanding is that much of the original handbook and magazine literature on these tubes was, well...wrong.
All the information here is openly available, but is scattered in different publications of different vintages and difficult to assemble in one spot. This is an attempt at consolidation.
Cathode-Driven and "Grounded-Grid" operationNo, they are not the same thing.
Screen RegulationIs terribly critical and nearly never done correctly, particularly in articles of 1950s-1960s vintage.
Heater OperationAbsolutely, Positively No More than 6.3 V...and preferably less
Cooling and Blower Requirements
These tubes are not easy to cool.
There is no such thing as a "1 kW 4CX250B" amplifier. Period.
A "1 kW 4CX250B splatter generator", maybe. But certainly not a linear amplifier.
Class AB1 means NO GRID CURRENT
And a Class C amplifier is not a linear amplifier.