It should definitely be possible now to get a previous build’s artifact through the API, but you might have to write quite some code for it; although it might not be possible to do it easier, as “previous build” might mean quite a few things, depending on the project, e.g. previous by build number, or previous on the same branch, previous using the same workflow, …
If you have any questions just let us know, we’re happy to discuss more about this and might even worth a Feature Requests topic eventually