ArcCatalog is a powerful tool for easily managing data. I haven't seen anything like the easy data management functionality of ArcCatalog in ArcGIS Pro. And the last thing I want to do is create a whole ArcGIS Pro project folder when all I want to do is look at some data that someone just sent me in an e-mail. If the end-game really is the extinction of ArcMap 5-10 years from now, then Pro will have to have a replacement for ArcCatalog.
Asking users to use ArcGIS Pro's project pane to manage all of their data is like asking Windows users to use MS Word's Browsing window to manage all their files. A browse window is no replacement for a full-featured data management app like ArcCatalog.
I'd like for someone at ESRI to acknowledge that and tell us when it will be added to the development schedule.
I'm actually really eager to begin using Pro routinely and it's frustrating having a major stumbling block like this in the way.
As this conversation has grown over time, users who are seeing it for the first time probably won't get through all of the comments. We're placing this statement (from June 2017) here for visibility and to continue to encourage you to share your input about needed functionality in the comments.
There's more discussion of this issue on this thread: