Most DAWs are concurrents. I have observed only several more or sell distinct DAWs: Ableton, Tracktion , (m.b. FL). All other are "fighting" on the same field. And any of them want preserve its own share of (as Craig has written many times) not so huge user base.
Different DAWs have different imagination how open they should be. IMHO ordered list:
1) Reaper. DAW generate C++ header file for its API. Basis libraries are open source. Developed by pro programmers, with very specific finance approach (no marketing, almost no design, no army of useless for the goal managers on S-Class). I guess other have a very good reason to "fear the Reaper"...
2) Ableton, Bitwig, (ex)Sonar. Relatively open, with API. Ableton Push 2 has complete documentation (not many modern hardware devices have that, but I should admit Novation publish documentation these days. May be Focusrite influence since they was not open before).
3) Cubase. They have made VST. And just for that they should not be at the end of the list.
4) ProTools. In general close, but since they are the "standard", many things are at least partially open (EuCON, HUI, there are converters for pt files).
5) Studio One... Have they made anything "open"? The investment into design and marketing is big. Probably they have learned how to proceed from Apple: make own eco-system, make everything simple, convince users that everything is exactly what users have asked for. "You do not need 32bit plug-ins". "You do not need hardware mixer in your audio interface". But read how well they write about that features (more precisely the luck of them...). You want to believe immediately