However, you can't really ask for a stamp if you're not passing over a border that has immigration control at it. And in any case non-EU/EEA/Swiss people don't want extraneous exit or entry stamps from Schengen countries, because the stamps might not tally properly, which could cause problems on final exit from the Schengen area.

Technically, EU countries are not supposed to stamp EU passports because (it is said) the stamp implies immigration permission to enter or leave the country and no permission is needed from an immigration officer. (I must say that I'm not quite why a passport stamp that that gives only the date, the point of entry or exit, and the mode of travel could be said inevitably to imply permission rather than simply facts...)

As you say, though, many passport control officers will oblige with a stamp if asked, particularly (though not only) in a child's passport.