With a cathode follower tube amp, the mic's transformer can be placed in the psu box, therefore reducing the size of the mic.I think this was their prime concern.
The cathode follower, as mentioned, makes it possible to do so because it lowers impedance electronically.
As Oliver mentioned, the cable makes a difference, because although a cathode follower has a lower impedance than normal for a tube circuit, it is actually subject to capacitance issues with aged cables, and interference.
The output transformer has a 10k resistor on the input winding, which means that it probably won't be subject to too much 60-cycle hum from the mains transformer.
If those are the original Electrolytic caps, you may try and place a new 10 or 20 uF cap in parallel to the last cap connected to the b+ power supply with alligator-clip connectors (mind the plus and minus if you don't want to blow up anything).
even though cathode-follower circuits are self-regulating, you may find a decrease in noise and a slight improvement in highs.
if you do, solder it in or go ahead and change the others, as they have probably never been replaced.
the E cap you place in parallel with the other will keep its charge for several hours if it's not discharged with a resistor or something so watch out! Don't touch the leads.
P.S.: Did you try to swap mics with psu's to see if the bass problem is in the mic or the psu? The psu holds all the coupling caps and output transformers, so if it's not the psu it has to be the capsule.