If it has been a trying day filling shelves or on a flight tending to difficult passengers, then a word or two showing appreciation of the fact should be given. Of course as you say, it is polite to say thank you to the CC, but why does it need to be done in front of passengers?
Saying thanks doesnt cost anything, and as SLF I have no objection to it being done in public, as long as it comes across as sincere. The airline where my daughter works fly some difficult routes and its not uncommon for the cabin senior or Cpt to use the tannoy to thank them, but equally they re inforce it at the debrief (or in the bar on a stop over!)
My wife manages a childcare nursery and makes a point of thanking her staff as they leave, normally in front of the parents, and it is appreciated by the staff.
Personally I dont think managers generally thank staff sufficiently, it costs nothing but means a lot. Whether it is done in private or publically is for me a non event as long as it is done!!!