Welcome to the forum!
I don't think it's possible to combine all of those. Because it doesn't work to apply the powerstroke to a closed path, which is what a Calligraphic line is - a closed path. I'm not sure if that's a bug or not.
If you use the Pencil tool, with the Triangle In or Out shape applied, the Powerstroke LPE is automatically applied. And plus, new with 0.92 (or might have been 0.91) there's an option to automatically apply the Simplify LPE (which is a live version of the regular Simplify). So that gives you 3 out of 4. Except that you might not necessarily what the triangle shapes.
If you draw just a simple path, with Pen or Pencil (with no shape added), you can apply the Pattern Along Path LPE (PAP can work like Calligraphy, in a way), Powerstroke, and Simplify LPE. That gets you 3 out of 4 too, and you choose your own shape (the pattern of PAP).
The problem is that only the Calligraphy tool can provide pressure sensitivity. I suppose if it were possible to make the Pencil tool have pressure sensitivity, you'd have it all at once, without the conflict between Calligraphy and Powerstroke.
I don't know how that would go over as a feature request. But I don't see why it wouldn't work. I mean, that's been a complaint from the very beginning about the Calligraphy tool, is the excessive nodes it creates. I wonder why it was chosen for pressure sensitivity, over the Pencil, in the first place? (Actually the Pencil tool can create oodles of nodes as well.) Maybe because that was the only way to get a variable width? But now that we have the powerstroke.....
Well, I'm not a programmer. But if Calligraphy was chosen for pressure sensitivity, because is can create the variable width. And if we now have powerstroke, which can create variable width for the Pencil or Pen..... Well, I don't see why not make the Pencil available for pressure sensitivity, and use powerstroke to create the variable width. Like for example, place a pink node where the pressure is greater, maybe??
Since Inkscape is open source, anyone can make a feature request, you're certainly welcome to do so. Now you've got me so curious, I think I'll ask on the mailing list whether it would even be possible. I'll let you know what they say.