I understand (b), and in fact I considered it a potential weakness, but why does (a) matter if you're selling from a single site? Even if you got multiple simultaneous orders, storing the last license generated in a DBMS should make it multiprocess-safe.
What do you mean by "predictably unique"? Do you mean "guaranteed unique"?
As a way to generate unique ids this isn't horrible. 12^62 is something like 220 bits. The odds of a collision are even lower than with a UUID.
Guaranteed uniqueness is preferred, yes. But the level of effort needed to guarantee uniqueness across a large application / dataset / etc is much higher than "unique enough", just as it's a lot more expensive to prove a number is prime than to generate a number that is 99.9999% probably prime.
That would be guaranteeing uniqueness. Don't bother guaranteeing uniqueness. The 99.99999% was an understatement. 12^62 is 99.999999999999999999999999999999999999999999999999999999999992% unique. This is higher odds than being killed by a meteorite.