So just what part of a rect tube shorts in the first place.
You should have started with this question.
A rectifier tube is a
diode, meaning it has only 2 elements (yes, an indirectly heated tube has an extra element, but ignore that for now). Those are the anode and cathode. In a rectifier tube, current can only flow when the anode is more positive than the cathode. Therefore, current flows in only 1 direction, and the output is always positive (in the case of your B+ circuit). The rectifier acts as a one-way valve.
Electrolytic filter caps have a polarity. The dielectric insulation between the 2 plates of the cap is formed by a thin layer of aluminum oxide that is formed by applying an electric charge in the correct polarity. If you reverse the polarity of the charge, that insulating layer vanishes, and the cap acts as a short-circuit.
Well, there's only 2 parts in your rectifier tube that are there to short together. Somehow, a sneak-path for current forms between the anode and cathode, other than the empty space between them. Now the rectifier is no longer a one-way valve, but current can flow in both directions with equal ease. Once that happens, the output is no longer positive-only; it outputs essentially the same a.c. as is coming into the rectifier. On the negative half-cycles, the electrolytic caps' insulation layer vanishes and
BAM... your fuse pops due to excessive current draw.
You pop in another fuse, and get another blown fuse. You change the rectifier and try another fuse, and everything's happy again.
... lets say the caps don't blow ...
I think I've demonstrated that isn't likely with electrolytic filter caps. It's possible, and it seems like it may have happened in your case. In any event, the momentary vanishing dielectric is the means for massive current flow when the rectifier shorts.
It
might be possible if you use those enormous plastic film filter caps (such as Solen), assuming the excessive current doesn't damage the cap. It very well might pop the main fuse before damaging the cap. Or maybe the cap dies too.
The rect tube changes a/c to d/c ...
It is important (to make sense of future symptoms) to know the rectifier
does not change a.c. to d.c. (at least, not by itself).
It takes an incoming a.c., which has positive and negative pulses, and converts that into a series of pulses in one direction only. Whether they are positive or negative depends on the direction of the rectifier.
The cap and load resistance attached to the output of the rectifier is what turns the pulses into something resembling d.c. The cap charges to the peak value of the incoming pulses, and the load resistance (if high) causes the cap to discharge slowly enough that the average voltage remains somewhat close to the peak value of the incoming pulse.
If the cap value is small, or if the load resistance is low (drawing a lot of current from the cap), then the cap does a poor job of maintaining its voltage level, and the output of the rectifier is mostly big pulses.