I think a CLI might be nice, but even then typos in code aren't such a big deal IMO. Sometimes they do come up with copy in UI code, but even then, NBD.
So for me, a spell checker in CI sounds like a nice to have, not a necessity.
Maybe it was just me but at my last role, I worked on a piece of software with a typo that stuck out like a sore thumb but the cost was too high to ever fix it (impacted multiple products with independent schedules or were just being milked and had no staffing).
I also remember some bike shedding over a person using a British spelling for a word instead of the American. Some times linters are just nice for deciding minutia so people don't argue (see also formatters).
However, I fully admit, compared to a lot of other priorities in software, these are minor.
Eventually we fixed it in our API gateway for the API we provide to customers because it looked unprofessional, so we have a mapping layer in that API that exists purely to correct the typo.
I mainly use JetBrains Rider though, and that has really good spell checking support built-in. Something I really like about Rider's support is that, just like lining rules, you have the option of saving additional words at the "Team Shared" level, so the whole team can use the same extra dictionary words. The same function works in Visual Studio with ReSharper installed, and presumably it's available in all JetBrains IntelliJ-based IDEs.
I also enable & use it with languages it doesn't really have proper support for (like sql and ruby) - just add words to the dictionary as they come up.