Could a vacuum tube computer be fast?

[Dave Long]

If I've done the math correctly, a single 955 acorn tube runs almost  
a watt for the heater alone, and then around 3/4 of a watt for the  
anode current.

Could it be that no one built small fast tube computers because their  
busbars would have melted down in sparkling, coruscating displays of  
incandescent brilliance ?

-Dave