Ok, I understand. I think the core problem here is that a particular PSF is valid only for a particular image, and there is no single image that covers the entire area of sky that HSC covers. There are multiple overlapping epoch-level images at any given point on the sky, of course, so even at a single point no one of those is "the PSF".
However, when we make coadd images, we coadd the PSFs in a way that is consistent with the way we built the coadd (i.e. it's the appropriate model for the effective PSF of the coadd). If you get the PSF object from a
deepCoadd_calexp image, that's what you're getting - but even those are only valid over a small region of sky, called a patch. All of the patches in a larger region called a tract share a common pixel grid (they're conceptually square subimages of a larger virtual image for the full tract).
You could conceivably make a
CoaddPsf that combines PSFs over a tract, but it would be very large and cumbersome to work with, because it would essentially have to store all of the PSF models and WCSs of all of the input images that went into all of those coadd images. I'm afraid it's not possible to make a
CoaddPsf that covers multiple tracts, because the class assumes there's one WCS that describes the pixel grid of the image to which it corresponds, and different tracts have different WCSs.
If you want one object that can return the PSF at an arbitrary point in the survey, then, I suspect you'll be better off writing a new class that can look up the tract and patch that correspond to a particular point in celestial coordinates, load the
CoaddPsf for that patch, and then evaluate the PSF at that point after converting it to tract coordinates. If you load the
deepCoadd_skyMap dataset (this will be an instance of
lsst.skymap.RingsSkyMap for HSC), you'll get an object that can do those tract/patch lookups and coordinate transformatoins.