Similarly, I've used this before:
https://www.digikey.com/product-detail/en/texas-instruments/TPS2491DGSR/296-26925-1-ND/2255225(there are also different voltage and cost versions I think)
And yeah, ride-through or short-circuit capacity is limited by SOA, which is in turn limited by physical size of the component.
Get the cheapest, lowest-Rds(on) D2PAK you can, and you should be able to handle a couple milliseconds of fault condition without trouble.
Consider that we're often talking hundreds of watts under a fault condition, while a transistor might handle a few mJ (small SMTs), tens of mJ (DPAKs), or hundreds of mJ (D2PAKs and THT). With power and energy figures like this, it's hard to have more than a few milliseconds of active operation before it has to stop, or it blows up.
There's not much you can do at the PCB/assembly level to improve this -- there's just not enough time and material to carry the heat away fast enough. You can improve the retry rate, with heatsinking.
You could also use simplified logic to go between a saturated transistor, and another (smaller) saturated transistor in series with a big fat resistor, to try and soft-start a load. This doesn't have the same dynamic range as the active version (pass transistor): it may deliver "too much" short-circuit current, and not enough startup current when the voltage drop is small (which means the switch still has to pull in the remainder, so should still be a linear current-limiting type!).
This isn't suggesting anything new -- startup resistors have already been mentioned in this thread. It's just another way of thinking of it: an array of switched resistors (including zero or one of them!) makes a few-number-of-bits power DAC, while a linear element is of course the analog version.
The advantage with resistors is, basically anything wirewound has metric shitloads* of energy capability. Apparently the TE Connectivity aluminum-body wirewound resistors can handle quite a lot of power, like 100J, at good prices. It's hard to find anything else that can dissipate as much energy per dollar of BOM cost.
*That's a technical term.
Tim