It's strange to have Ardour and Reaper up there with ProTools and Logic described as a MIDI sequencer. That's how it started but at some point it crossed over into a full-featured professional DAW and I'm not sure even Reaper has caught up to its live instrument mixing and editing capabilities.
Ableton is literally a sequencer (and much more) and probably belongs in your MIDI sequencer category.
No, the point doesn't hold up. That's like saying 'workbench' or 'car' is too general to mean anything. It's a general category and you put adjectives in front of it as needed.
And if you're going to eschew the term and use descriptions instead, then it's important to get the descriptions right and not arrange them just so your favorites are up top next to ProTools even though they don't belong there.
Better categories:
Professional DAWs - these do everything well: ProTools, Logic, (maybe) Cubase.
Consumer DAWs - these aim to do most things well: Reaper, Ardour, GarageBand.
Sequencers - geared for hip-hop and electronic music: Ableton Live (yes, it's awesome and will probably become full-featured), Fruity Loops.
Trackers....
My point is being fussy about the term DAW derailed GP's question, when they asked if it's a DAW they're asking if it's a general purpose or specialty platform which is frankly a good question.
I said not all of these things should be called "DAW", but they are all called DAW by many people. I'm saying that is confusing terminology and I wish we could settle on calling some of these things something else. I don't care which things get called "DAW" and which ones get called crows or other types of corvid.
But, the term "DAW" is overloaded, and one of the negative side effects of that overloading is that whenever the discussion comes up somebody has to argue that a bunch of these things that people call "DAW" are stupid and we should hate them because they aren't good for X, Y, and Z. As you have eloquently demonstrated.
Were you trying to demonstrate that fact?
Also, I not only had no intention of derailing OP's question, I answered it by explaining that Radium is in the "modern tracker" category.
To be clear, I'm not agreeing with you and it's bizarre that you think I am. The term DAW is just fine, it's not overloaded and I found grandparent comment's usage of it to be perfectly clear.
Rereading your post I see you did put Radium under your 'modern tracker' category, I think I was so appalled at how you described the other products that I didn't pay attention to where you put it because at that point you had already demonstrated the depth of your knowledge.
Ableton is literally a sequencer (and much more) and probably belongs in your MIDI sequencer category.