Almost everything you do on the site will leave a public artifact, what remains is the level of detail that ordinary users can see. This sort of transparent, fully public operation was a key design decision and considered to be critical for a sustained self-governing community.
'Favorites' has been a somewhat misleading term. It basically means "I want to find this easily in the future, and know if more things happen here." People use them more like waypoints than an indication of enamoration. The only valid issue I see with them being public is presenting them as "This user is enamored with the following posts:" when in reality, it might be more like "This user is actively watching the following trainwrecks:"
Showing your 'last seen' time is the simplest means of showing some kind of presence indicator on the site, which is very helpful when someone is debating on staying late in the office to see if you reply to their comment. If you haven't been seen in six hours, well ..
I am not at all opposed to changing that to a less explicit presence mechanic, but every useful one I thought of wouldn't be terribly difficult to reverse and allow folks to pretty much approximate the last time you were seen on the site. I'm open to suggestions that provide less precision, but also makes sure the intent in showing it persists.