Personally the reasons I like ML capture approach:
1) It sounds exactly like I want it to, right off the bat capturing my own gear
2) It lets me focus on using the real gear I want to at home and for recording (and even live) without worrying about having to recreate them on modelers.
Importantly, they help in separating my mind "live" from "home/studio" which is something I've struggled with in the past. I've been a fractal user for many years and I've always appreciated the complexity of the models, but I do find it easy (personally) to fall down the tweaking rabbit hole trying to best my real amps with it and spending too much time trying to decide if something is "better". I appreciate the relative ease of just being able to get the sound I want by capturing what I already like, and the ability to prove to myself that it sounds identical to its source definitely helps my brain stay grounded a bit. From there and if I have a good set of captures, I personally have zero issues using EQ to get where I may want to go even if it doesn't do the same thing as the amp's tonestack.
tldr the reason to use captures vs modeling is personal, rather than objective for me. Currently building a live NAM rig that's smaller than my FM3+tonex board to see how that goes