Using a lamp limiter is usually a bad idea with switching power supplies because of their negative resistance input characteristic and operating them at low input voltages can result in exceeding the current rating of the power switch and operating it at a high duty cycle. This points directly to a major cause of failure; if the input capacitor wears out, then the low average voltage at the input causes the power switch to fail which usually causes other damage.
Oddly enough this failure mode probably does not apply to the early 2215 power supply which uses a TRIAC based preregulator.
A well-designed SMPSU will have protection against an input voltage that is too low. Designers picked up on this fairly early on, as brown-outs are obviously a serious issue in some parts of the world.
But honestly I can't say if that applies to the 2215 as I haven't studied the circuit yet.
Also, be aware that faults in power supplies usually "cascade". It is doubtful that there is one single failed component - there will be a chain of destruction that will often result in new components instantly being destroyed at power-up (the lamp-limiter will help to an extent here).
Tektronix was pretty good about including crowbar circuits in their power supplies to prevent catastrophic failures from progressing to the low voltage side. The later 2215 power supplies includes this but the earlier one rely on a shunt zener diode. In either case the crowbar or shunt zener diode should be checked.
For clarity, I didn't mean this. Perhaps "cascade" wasn't the best word exactly; perhaps I should have provided more explanation.
I was referring to the PSU on its own. Often, if the switching transistor fails, it can take out many other components near to it, such as the control IC, the current sense resistor, perhaps many other things.
What happens here is that the service guy spots a shorted transistor, changes it without making other checks, and the new transistors fails short in the same way. So next time, one of the other faulty components is spotted, but now, two new components fail again at the first power-up attempt. Repeat until madness sets in

It's fair to say that switched mode power supplies rarely fail in an over-voltage condition. Most include a crowbar by default, of course, but generally failures stay within the PSU in most cases. Happily...
Away from that minor clarification, I happily agree with everything you say. Yes, capacitors are the usual enemy. High-value resistors in the start-up circuit can be another common problem. Both these are easy to diagnose and fix, but blow-ups are a different matter, and generally require a much deeper level of understanding and diagnosis skills. Sadly, I know that at least one of my 2215s has had a blow-up, so I'm not looking forward to tackling that - and I say that as someone with many years of experience with these things

All the best,
Mark