I agree that separating the seat from a locked bike is something many do as a theft deterrent.
If that's what you want by not including the seat+post with the bike in the travel case, maybe keep the seatpost with the bike, and carry the saddle with the carry on. I can't see any saddle from being denied, whereas the seatpost can still be a "weapon".
I'm also assuming you don't have any check-in luggage other than the bike, so everything else is in the carry-on (a lot of people travel like this).