Contractors or tradespeople are generally licensed at the state level, but permitting is done at the city or county level, where it's even done at all. Permitting varies by jurisdiction, where some don't ever deal with homeowners (i.e., the contractor applies for and gets the permits), while some will (though maybe they prefer to deal with the contractor). It also varies widely in what types of work even need a permit.
AFAIK, various building codes (e.g., the NEC) do not say anything about licensing, meaning each state sets their own criteria for granting a license (if they even have licenses). The state is also the one who enforces the licensure, not the permitting jurisdiction(s) - this is why your comment about the city revoking the license wouldn't necessarily work; the city could alert the licensing agency, but couldn't actually revoke the license. See e.g., this sting in Houston, conducted by the Texas licensing department and not the city of Houston or Harris County.
In your specific question, I flagged it as off-topic for three reasons really:
- The question of who is supposed to pull the permit (if one is required) varies at the city level; this SE just doesn't get down to that level of localness, especially since no location was even specified.
- Licensing is a state thing (spelled out in laws), not a building code thing.
- The legal aspect also came up because (in jurisdictions where homeowners are allowed to apply for permits), this would (should) be a point addressed in the contract.
As far as updating the help page, I think the page is pretty clear, as these two points in particular apply to your question (emphasis added to highlight specifics):
- Local building codes or advice limited to your area.
- Legal questions, including contracts with builders, contractor negotiation, and rental agreements.
Maybe it would make sense to change the second one to "Legal questions, including permits, contracts with builders, contractor negotiation, and rental agreements.", maybe not.
However, not all questions about permits are necessarily off-topic. For example, the last line in your question, "Can a licensed contractor perform work, that requires a permit, without a permit?", I think is probably on-topic (with a very succinct answer of "No"), since that is a generally universal aspect of permits - if they're required, you gotta have one, regardless of who performs the work. This is the inherent ambiguity of the help page, and why your question is still open - just because I, or @isherwood, or @DanielGriscom think it is off-topic doesn't necessarily mean the rest of the community does.