The SharePoint 2013 List View Web Part’s toolbar type setting is something of a clumsy ninja, brilliant but clumsy nevertheless.
The problem is, the toolbar type property enumerations bear little resemblance to what you actually get, and in one case just blatantly lies..
Drag and Drop
Drag and drop of files onto a list view web part is possible with all toolbar types. In some cases you may notice that you can’t drop files onto the web part, I’ve found that resetting the web part view in most cases fixes this issue.
If it doesn’t, then check out this post by Hristo Yankov (@hyankov) which involves adding a small script to the web parts JSLink property, and this post here also talks about the inability to drag and drop files.
And so, to abate further clumsiness the toolbar types and what you actually get is as follows..
Getting retro with the toolbar we know and love from 2007 & 2010