I've repaired a few power supplies over the years. I've been lucky that I've only personally fried one lab supply: an Amrel unit blew an internal diode when I tried to charge an almost dead car battery. I probably swapped the leads but I wonder if I didn't set the output voltage too low and if it had a down-programming circuit, maybe it tried to discharge the battery.
One of my little Lambda supplies, an LP-412 developed a flakey voltage set pot that caused the output to spike to max regardless of the setting. Turns out that when the output voltage is greater than the set voltage, the supply's design shunts the reverse current thru said pot. If there's a large cap or a battery on the output and the pot is set to a low resistance, it draws a large reverse current and burns a spot on it. I added a PNP power transistor to the external programming terminals that shunts the reverse current away from the pot thus protecting it.
Most recently an HP6002A that I got because the previous user couldn't repair it. After one of the paralleled pass transistors and the downprogramming transistor were replaced, voltage mode worked but current mode was really unstable with a crazy sawtooth waveform. Turned out the original LM301A opamp had been replaced with an OP07 precision amp that caused one of internal DC busses to oscillate. I recall also swapping out an LM358 for the correct LM1458 - both dual op-amps, but quite different characteristics.
I have a question for the OP joeqsmith: what zener diode has died on your supply? I ask because I have an hp6284A which is from the same family as the hp6289A and when I looked at the '89A's manual from Keysight, the last page covers a design issue that appears very much like the down-programming issue above.
I have an hp6012A 60 V, 50 A switching lab supply that has a problem with current limit. I haven't needed the supply for a while so I haven't spent time on it. I wasn't too impressed with some of the design details and see that hp revised it to 'B' fairly early on.
I've repaired a few Tek and Wavetek function and pulse generators over the years. One common user generated failure is that the output transistors, usually 2N3866/2N5160s are bad. These are getting pricey so I bought a few extra last time.
In general, I've seen electrolytic caps open and tantalum caps short in all sorts of equipment and especially in stuff built more recently. So far, I haven't seen any power line X & Y caps fizzle out but I suppose it'll happen sooner or later.
Cheers,