Edit: But I'll concede that when your outputs are only four characters long and end users will actively interact with them (write them down, type them again later, etc.), additional safeguards might be appropriate. Or simply omit all alphas and use only numerics.
You're still not out of the park with numerics - people with 1313 or 6660 or 4444 or something will complain a lot. The possibility of a 666 in some new biometric government IDs in my country rose a massive stink from church...
Yeah. An important, long-lived ID that will stick with an individual for their entire life, and that they may want to commit to memory. That seems like a good time to take a hypersensitive approach and adopt some kind of filter.
Also, have a feelin you meant to do 1312. What’s the issue with 4444, though?
That works pretty well until you realize that some numerical combinations are common neo-nazi codes and may lead to ... unfortunate associations. The ADL lists a few of those^1, but the list is by far not comprehensive, codes actually differ based on locality, and accidental combinatory collision in a 10-character space than it is in an alphanumerical 36-character space.
[1] https://www.adl.org/education/references/hate-symbols/88