When saving PDF files, Skim requires full navigation from the user Home folder every time, rather than recalling the last folder saved to. This is something that would be useful as a user setting to turn on or off as desired. Either remember last folder saved or not. The current system wastes significant time re-navigating the entire path every time.
The saving is just standard behavior. In fact, the save panel is run and prepared by the system. I don't think we should override the standard system behavior, I see no pressing reason.
Certainly it is not worth another preference setting.
Apart from that, this is not what I am seeing. For me, the last chosen folder is selected the next time. So that does seem to be the standard system behavior.
If that does not work this way for you, that would be more a problem for Apple.