I understand, yes, how the present perfect can sound more formal. I see what you mean. I simply was not taking that into account.
I see what you mean by comparing the simple past with the present perfect in the way that you did.
However, the idea just didn't occur to me. I can, however, easily take note that the present perfect would be used in circumstances which might be considered more formal as you have shown. However, I wouldn't think that it has to be that way all the time.
I personally don't know why I would want to be careful about how I ask someone about "eating lunch".
Have you eaten? - Yes, less direct. I see what you mean.
Did you eat? - Yes, more direct. I see what you mean.
I'm not so sure that many speakers would make a decision to use one or the other based on any sort of social deference, however.
Know what I mean?