Actually, the channels>layers can produce results that are near impossible to reproduce using adjustment layers...
See, if you start with a color image and use the B&W adjustment, Desaturate, Channel Mixer, etc. you get a global conversion to B&W.
There is no easy way to have local control how the conversion will be handled...you can't use layer masks because, well if you mask part of the adjustment layer, the reveal will be back to the color image and trying to place yet another adjustment layer over it becomes problematic...
In terms of B&W conversion in the raw processor, same global deal.
Where the channel>layer is superior is that you can literally paint in a custom B&W conversion area by area and use masks to control what layer are visible. It's pretty easy to do an action that will do the base conversion for you and add hide all layer masks so all you need to do is choose the layer and paint it in via the mask.
I won't claim it's "the best" way...I often do B&W conversions directly in Camera Raw or Lightroom (usually Lightroom where I can make a virtual copy and keep the color & B&W separate). But if you need precise control over different areas in a B&W conversion then the channel>layer is a good solution. Of course, one does have to know how to do it...
My typo didn't help, but notice you quoted my saying "one
or more adjustment layers". If you don't want a global conversion but do want to paint in custom conversions, then the second or later B&W adjustment layer would apply its conversion recipe only to whatever colour shows through after the initial, masked B&W adjustment layer - your "reveal". The topmost adjustment layer would need no mask (to be sure that no remaining colour is peeking through). So I'd have the image as a raw file smart object, plus local conversion with 2+ masked adjustment layers.
Where's the advantage? Well, to some extent we're different rather than better. Assuming we're both staying in high bit etc, we'll both end up with the same best quality data, and we don't care if your 3 pixel layers plus masks result in a bigger file than mine (the SO probably makes it even anyway). We can assume your action included a colour layer, so you can always output the same file as a colour image as easily as I can by switching off my adjustment layers. We'll even take the targeted adjustment tool's virtues out of the comparison. And let's assume in each case one does indeed know how to do it....
I'd say the main difference is in flexibility, which is key because you don't always get things right first time. Let's say that after making the b&w conversion one wants to do something like tweak the lens vignetting correction or adjust capture sharpening or noise reduction - I'm going to find that a lot easier as my adjustment layers have entirely separated the b&w conversion from the image smart object which I can tweak in ACR. That advantage is even greater if one wants to do more substantial in-Photoshop retouching, whether that's cloning or something like perspective or lens correction. Again, the adjustment layers would provide flexibility that your pixels layers can only provide if one really, really knows how.
The end results can be the same, but the workflow's much sweeter.
John