> The peak currents can be very high as C is made overly large. To the point of destruction.
Peak current is limited by ripple depth and transformer resistance. Not by C, not by load. Pick your diodes bigger than your transformer rated current, you will usually be fine.
Rectifier RMS current rises fast from small to medium caps, but slow from medium to huge caps. In almost any audio situation, your RMS is nearly as high with a "good enough" cap as with an over-size cap.
Duncan's Power Supply Calculator is the modern way to figure this stuff. The hard part is getting real-world values for transformer parasitics.
Hyper-low ripple just won't happen. It is diminishing returns even with ideal parts. With real parts, "negligible" resistances become real problems. An inch of cap lead in common between rectifier circuit and load circuit, 0.01 ohms taking 100A peaks, will inject 1V of ripple to the load even if the internal cap voltage could be "dead-steady". You will almost never get to 1% ripple (maybe on very small projects where over-kill is cheap). For simple tube-work, you get a few-% ripple and then add an R-C. This not only doubles the rejection slope, it rejects the parasitic ripple on cap leads. To go further, add another R-C for every 20dB-30dB of ripple reduction you need; trying to get 40dB in one R-C is usually frustrating and also more expensive than two 20dB R-C networks.
I have a 30V 60mA D-C-R-C-R-C supply which feeds directly to a low line-level input (simplex audio+power). One more R-C to the mike capsule. There's not a lick of hum/buzz in it. To do this on one stage would need a 60F (yes F) cap with 10 microOhm lead and internal resistance. Bigger than a milk-crate and over $10,000. My way was $13.
I'm puzzled by your blown-open transformer event. Yes, the one winding was taking double surge current. But unless the cap-bank was too big to fit through the door, the surge should not have lasted the many seconds it takes to melt heavy copper. I wasn't there, but from a distance I wonder if it was just connected wrong, or very marginally designed. I've been around similar events and sometimes you just can't tell after the smoke clears.