There needs to a middle ground. While it is true bad APIs need to go once in a while, a lot of them never should have come in the first place, and if some work had been put into getting them right in the first place they would still work just find today. Not perfect mind you, but just a little effort would be enough that we wouldn't have to deprecate them.
I think the Web is moving in this direction, though I don't know how well.
Flash is a zombie but not dead. You can still get an old swf working by clicking a couple of things in browser settings. The thing with google is they deprecate wayyyy to fast without proper thought to the alternative. It's like their projects commit suicide than die naturally.
I think the Web is moving in this direction, though I don't know how well.