Will self etching primer etch chrome? I tend to think that it won't, but I really don't know for sure. I used to use Metal Prep, a liquid etcher that is used before priming. That's the old school way. It doesn't appear to do anything to chrome. It may be that it has lost its effectiveness. The bottle has been in the cabinet for at least 25 years.

The primer is not just to fill imperfections. Primer sticks better than paint does.