When the hum is there, can indicate several things.
Loose wind.
Poor rectification - Diode may be going leaky...
Filter caps bad...
Cherokee CBS1000 - I had, "hummed" all the time - replacing the caps did not help.
Found out later the issue was with the power transformer.
Cost too much to replace it - so bartered it off. (pre-2006 - so now there are switching power supplys that could possibly have replaced it...not back then)
The power supply in the base, is a Linear-type so it will always "draw power" and yes, if parts fail - depending on what can fail - magic smoke will erupt. The cap 10,000uF 35V, the Diode Bridge - there is also several Zeners and a disc cap or two - along with the power switch - that is on the output side of it.
Nomad helped me understand this better...
So If I get this wrong - its' on me because I didn't listen...
Between the two there are very little differences in theory, only the Uniden uses the GROUND to remove the bias off the regulator feedback side - no bias, no regulation - dead...kinda' thing. In doing it this way, you still have a liability but the + line output is nearly at zero. This can help if you have a filter cap preparing to go out.
Now, in looking at the above, you can see there are very STRONG similarities to the AM regulator used in most of SSB radios today.
Just some thoughts...