Is it possible to save a swatch library as part of a PSD file? I want to open PSD files and have my color palette in place. Seems very logical to me.
As far as I know, no.
The swatch panel works on an application level, not a document level, so I doubt there is a way for this to work. Switching between open documents doesn't change the swatch panel.
You can save your swatches to a file. If you save the swatch to the Presets/Swatches folder, the swatch will be available in the list of default swatches so you can easily load the swatch when needed. Or you can just save the swatch file to the same project folder with your PSD and open it at the same time, it's not that much extra work to open the swatch too.
In CC you can now save colors and color groups as Creative Cloud Library assets. No need to worry about swatch files or anything else, your colors will be available to all your projects all the time.