I'm very eager to start working with the beta of Publisher. My background: for years I made my living using InDesign, Photoshop, and also some Quark and Illustrator. I've been looking to replace the Creative Suite for the typical reasons. I purchased Quark 2015 recently but I must admit it's still pretty clunky compared to InDesign.
I would want Publisher to have a very intuitive capability to Zoom view in and out and also rapidly shift between tools and back and forth to the zoom and pan functions. You want to be able to quickly move in, out, all over a document, change tools rapidly and shift through all these functions very quickly. It should be able to control character, paragraph etc styles very easily. It should be able to deal with image opacity, resizing, editing, and masking very easily. Create, assign and modify master pages. Obviously it would need to be able to export to finely controlled PDF types for different print output. I would guess at a basic level I would want to see it import and export Quark and InDesign files, although as long as it basically works well this is not a deal breaker... It sure would be nice though! Quark 2015 does have the ability to assign keyboard shortcuts to a broad variety of functions, that is pretty nice. It can also create static layout ebooks, although the workflow seems particularly awkward even for an advanced InDesign user. Those would be nice features to see in Publisher. As you would guess since I keep referring to it, a fast workflow is key.