They're useful in exactly one situation: when you have a temporary secure communication channel, and a long-term insecure channel. Then you can use the temporary channel to pre-share a lot of key material (say, a 1TB micro SD card carried covertly) and then use that for future messages. But that scenario is very rare.
"Our main cargo is a one-time cryptographic pad. The source is Commercial Security at Sjandra Kei; the destination is the certificants' High colony. It was the usual arrangement: We're carrying a one-third xor of the pad. Independent shippers are carrying the others. At the destination, the three parts would be xor'd together. The result could supply a dozen worlds' crypto needs on the Net for ..."
I don't really think the parent comment understands that there are creative ways around the difficulty of sharing secure pads. We don't need it for all data; but I think Vinge does hint at a totally viable means of sharing, and scenario in which it's practical.
Key exchanges would be annoying, but they are even more so for one-time pads.
But it will never come to even that: There are plenty quantum-safe asymmetric cryptosystems around.
If we were serious about it, sharing flash drives and even using couriers could make it work pretty well.
Seems like we should have figured out a way by now to use one time pad encyption by default for critical paths, even if that requires new industries to distribute pads and guarantee their security.