A capacitor (or other component?) going bad could damage a charging device, and will happen more often with older AC/DC adapters.. But if no component issue, probably not.

If the port is out-of-spec, however, that’s a different story, regardless of age.

(The OpSec angle on public chargers… almost certainly extremely remote and should not be a concern due to in-built controls on phones, but I too don’t plug into them directly. If needed,

I plug my power bank into the charging port, i.e. put a ‘dumb’ device between the public port and my phone, then pass-through to my phone, but would just prefer to use my own charger.)