I don't know that print sharpening even can be previewed on screen - the resolutions of the two devices being so very different. PK Sharpener uses an algorithm for print sharpening that is supposed to be "scientifically" correct based on the physical nature of different papers, inks, and the human eye at different feature sizes.
I've heard that argument before, and IMHO it's only partly valid. It's probably also why some applications do not bother to give a useful preview.
However, it is quite well possible to get a good impression about the amount of sharpening needed visually, when the resampling can generate a properly scaled preview, and that scaling is now available. I can go into much more detail (about artifact free resampling, viewing distances, medium surface diffusion, etc.), but that's perhaps going to take too much focus away from the general discussion at hand.
Suffice it to say, if we are going to down-sample the very finest (1 pixel) detail in our image by, say, a factor of 8, then we can't see it anymore if that pixel becomes significantly smaller than one output pixel. However, the 8 pixel large detail in the original image may become very high resolution 1 pixel detail in the output, so we need to sharpen with something like an 8x larger radius (if that is a meaningful parameter) if we can only view our original size. That's much harder to mentally envision than something that's properly dimensioned and only will vary a bit due to ink diffusion in the medium. That latter difference is quickly learned in practice, and is basically the only thing Lightroom (and probably Capture One as well) does.
I've also dealt with significantly upscaled output, and different things play a role there (including lack of resolution for reading distance viewing). But there are solutions that differ depending on the sharpening that's available.
Finally, there are sometimes innovations that go unnoticed for large groups of people. One example is the (also used for Smart Output) sharpening technique using so-called "Deep Focus Sharpening" that Mike Chaney developed for his Qimage Ultimate software. That is a completely Halo free output sharpening algorithm he developed, and it works great.
While I do not necessarily agree with the artistic choice of radius shown in
this video, it does demonstrate the effectiveness of the algorithm (without the need for halo masks or such), and it works very well for printed output.
The premise is simple, if no artifacts are created in the image, then no artifacts will show in the output, WYSIWYG. It basically just becomes a matter of amount if the radius is adapted to the output size and viewing distance.
Cheers,
Bart