In my experience Picasa only stores another copy of a photo if you tell it to.
People who "like" to keep photos still on their cards are almost certainly doing so for a bad reason. They should be disabused of their foolish notions rather than pandered to with software features.
Last but not least, Google Photos does do face recognition, plus "object" recognition: https://support.goog...answer/6128838?hl=en
Facebook does face recognition as well, though it's not really an appropriate replacement since it's public by default and has no editing tools. Flickr has some "recognition" stuff but it doesn't yet do individual faces (i.e. your great aunt Gladys vs. your uncle Bob). It will just recognize that there are *people*/faces in a given photo.
OK, I lied about that being the last thing. Personally I don't use Picasa anymore, but I really did love it for its face recognition, and also found it really useful to recommend to many people as a simple, easy to use *local* photo organizer and simple editor. Google Photos has limited storage space unless you cut down the resolution of your photos or pay for more storage, and that sucks. As local storage gets cheaper and cheaper, it's still really nice to be able to store photos on a hard drive! Of course I realize it's only a matter of time before that balance will probably shift, where having anytime, anywhere access is better. Even now the issue of cross-platform photo syncing is a concern that Google Photos helps manage (though not very well on desktop, in my experience). So... yeah, I'll miss Picasa, sad but not surprised it's being discontinued.