> Well, in my mind there must be a limit...
In normal operation, just be sure Vin-Vout is less than 37V.
Note that the main reason you use a regulator is because Vin varies!. So you have to think about the extremes.
If you wanted 100V out, add about 3V for the minimum I/O difference needed to give the chip something to eat. This has to be the depth of the ripple voltage: if you have 10Vp-p ripple, you need minimum nominal DC of 100V+3V+5V= 108V. If you also see +/-10% line and load variations you need to aim at 120V nominal. Low day: 120V*90%= 108V. High day: 120V*110%= 132V. Then you still have at least 10Vp-p ripple, so the peaks are 5V higher: 132V+5V= 137V. So you can do 100Vout with 10Vp-p ripple and +/-10% line/load wobble, and be just inside the 317's 37V spec. (This assumes a custom transformer wound to give exactly 120VDC at nominal line and load!)
Now short the output (stuff happens). The 317 will have 120V in, 0V out. The current-limit will try to turn the 317 off, but the over-37V will try to turn the 317 ON. The 120V on a 37V part wins, you lose. Instead of peacefully turning off to live another day, it turns ON, absorbs all the energy in your main cap, dissipates about 1,000 Watts, and bursts in about a milliSecond. You lost your $2 bet. (Could be a whole lot more, if the musicians were in a groove when someone dropped his keys in your only power supply.)
Note that a regulator (almost) always starts-up with a "shorted output". We usually have some capacitance on the output pin or out around the stuff it is feeding. The input voltage goes up, usually pretty quick (wall outlets have POWER and a transformer can pass a lot of energy quickly), while the output cap starts from zero volts. So at start-up you have both full input voltage and maximum limited current. If the load cap is small this may not smoke the chip.
A well-built well-boxed Phantom supply is "sort of safe" because a short on the far end of the 6K8 resistors should not drag the 317 out of regulation, and if it does there won't be any infinite current or power to pop the 317. But this assumes all accidents happen on the far side of the 6K8. In DIY, that is not always a safe assumption. Of course in DIY we can always fix it, but we may not have a spare 317 on hand at a hot Saturday night gig.
A 35V Zener across the shorted 317 will keep its I/O voltage within bounds, for a while. But even a small transformer will soon smoke a 1W Zener, and then we are back to the over-volted 317. As Dan says, a "panic resistor" is a great idea. It should have low voltage drop at normal loads, and burn-up quick and clean in a dead-short. True, you've just changed the repair from a $1.20 LM317 to a $0.30 resistor; but a dead 317 looks fine, a burnt resistor is pretty clear, so troubleshooting is faster. And your nose tells you right away what happened: with a dead chip there is no clue so you will waste time checking cables etc. (In Dan's commercial products this has the added benefit of telling the idiot customer why it failed. If the chip just pops, it is a mystery and probably "crappy product". If you stomp a wire or drop coins through vents and 3 seconds later smoke pours out, the customer may realize the cause/effect.)
A more clever trick is to put a high volt transistor above the 317, biased 5V-30V above the 317 output. Use an H-sweep transistor and you can eat 1,000V this way. But in a short, the dissipation in the transistor is high and not self-limiting. With very clever electrical and thermal design, the 317 can sense the pass-transistor heat and tend to shut-down, though with a hard short on a fat cap this may not be fast enough.
And if you pull out all the stops, remember that heatsink insulation has limits. You usually need sinking at HV (unless current is super-low) and you usually do not want HV on the heatsink (specially in DIY). You can use a mica insulator or buy the plastic-coat TO220 package regulator, but somewhere around 500V-1,000V these insulations can break-down (sooner if you get fingerprints and dust in there).
Remember: the 7805/317 regulators were loved when they came out, because designing a blowout-proof regulator from scratch is a Big Problem, and they solved it. The 7805 and 317 and their kin changed regulation from a troublesome specialty to a commonplace thing. Not for first-cost (early regs cost more than a few transistors) but because you could NOT blow them up as long as they never saw more than 37V. Just this one small thing to avoid, and for most 5V-15V work it is not a problem to be sure you never have more than 35V worst-case available. But ask for more than about 24V, and you are back to the bad old days of actually designing a blowout-proof regulator.