From the picture you sent,[A] it looks like there is a virtual “lintel” formed by a row of cabinets descending from the ceiling. If there is no lintel above the countertop, it does not require a mezuzah. Maybe that is the case in the rabbis’ homes you have been to.
If a cabinet, at least ten tefachim high, is under a lintel, and it forms the right side of an entrance to a kitchen, a mezuzah should be placed on the top third of the cabinet.[B]
There is room to exempt this opening from a mezuzah altogether, not because it is unfamiliar to see a mezuzah on a counter, but rather because the opening has neither a door nor a left post. However, as I explained in the introduction, it is common practice to put up mezuzot in doubtful cases since mezuzah is a Torah mitzvah. Yes, this may be called a “chumra,” but not “just a chumra.”
If the counter wall is less than ten tefachim, and there is no post on the right, only continuous wall, no mezuzah would be needed. If there is a post on the right, the mezuzah is placed on it, even if it is recessed many feet.[C]
 Agur B’ohalecha 23:20; Leket Shut Mezuzah 2:7, citing oral ruling of R. Eliashiv; Chovas HaDar 7:22; Pitchei Mezuzot 289:2:22.
 Chovas HaDar 8:2:3; Agur be-Ohalaecha 22:21-26.