The Montage is a computer. I think that the question would be better phrased as "why use a specialized embedded computer which is fully enmeshed in a MIDI controller, rather than a generalized desktop/laptop environment in tandem with a separate controller?"

This phrasing alone might help to answer the question.

It's preference. Preferences vary wider than there are solutions to fulfill those preferences. So you have many products that are examples of integrated MIDI controllers + tone generator of some form(s) + "other stuff" packaged in (sequencer, sampler, etc). And many products that fill the software/plugin category without an integrated MIDI controller. And out of the "infinite" possibilities - there are still at least twice as many visions of what people would want.

So - to cast one opinion in the bucket of infinity:

I choose an integrated MIDI controller with a "hardened" tone generator (with limited expansion for 1st/3rd party libraries) because:

a. I "trust" hardware more than software. I gig. I don't have the funds to buy redundancy in case my rig fails. I don't like fooling around with the setup (OS, software, packages, etc) in order to keep the lights on as much as I like tweaking the sounds within the more limited "rails" of dedicated hardware.
b. When I "turn on" the device - I want to minimize wait time. Computers are much faster at booting today. SSD - etc. So this is becoming less of a difference. And some keyboards are better than others. Montage's delay between flicking the power switch on and playing notes is quick. I don't have to do any work to get to this. This one may not be a clear differentiator.
c. My past gear has been from EX5 to Motif/MO line. So the commonality with past gear (architecture, parameters) was a deciding factor. Software has much less overlap with my past rigs.
d. Control surface integration. The "patches" of an integrated keyboard controller map out to sliders, dials, wheels, etc. in a much more fluid/sensical way than trying to retrofit a controller to software. I once considered just getting a "great" MIDI controller and going either rack hardware or software for all of my sounds. But cost wasn't going to be any better and I didn't like what I perceived was some lack of integration between the two domains.
e. Cost. Software can be cheaper - but there are some heavy cost hitters out there. And if your choices are unlimited - then, without discipline, the costs can end up being unlimited as well. Then perhaps you need more memory - so hardware needs to be beefed up. Faster SSD. Etc. Theoretically the software route costs are lower - but it's still an open system that allows for costs to be open ended as well. Hardware route - I don't generally get 3rd party libraries - so the cost is fixed. In general - more fixed by nature of the more limited choices.
f. Support - hardware support is more focused. Out of the software out there - apple software would be the next focused. Because apple has less variation in hardware. Still, there are still variations (laptop vs. desktop vs. this OS and that vs. all the different software packages). With hardware - and since I'm a live player (not necessarily using the DAW integration) - my support needs are "one stop" - with this box that makes noise. With hardware - there's the PC manufacturer as one source of support, the various software packages - the operating system (if different from PC), etc. The support model is less focused.

This is all for live use.

For composing, I wouldn't need to use the same setup. I don't need as much integration of the knobs and dials - I'm not really crafting sounds at that point. I can dilly around with the computer more. But generally, I don't care what sounds are coming out. I just use a "piano" and notation software. My "piano" at the desk isn't my gigging synth. It's 88-note and happens to be an integrated tone generator + MIDI controller. But I could have anything there - even synth action. I've got my computer there, an audio interface (4 XLR), etc. So I'm not "either or" - I've got both. I do have a "dumb" MIDI controller that I haven't integrated yet.

I don't use my keyboards for backing tracks of anything. In the sense that I don't have my keyboard fill the role of drums nor do I have the keyboard play much that my fingers are not playing. I don't use ARPs outside of triggering a harp flurry of notes - not what I would consider "backing track".