The contrast of paper, in your case canson baryta is about 250, may be between 250-300 assuming your canon printer can deliver deep black. Your monitor is probably more in the range of 700-100. So yes dramatic contrast reduction(blacks, less black)
I thought that prints were limited to the reflectivity of charcoal (2%) and perfect paper (100%) to a 50:1 or less DR?
Does a print wrt colors/tints etc, including the colorshifts look sort of the same to the softproof result?
If so then the printerprofile for that paper-printer combination may have a coloshift problem.
To my eyes, yes. So am I right in assuming that profiles/color management generally tries to keep hue (as constant as possible), while reducing saturation as needed in order to fit one color object into the limitations of an output device?
Also the baryta paper is in certain areas capable of handling more saturated colors (bigger than aRGB) than your monitor can display (i do not know about your canon printer, but in case of HP B9180 or Epson4900 it certainly is).
How your monitor displays colors that are out of its gamut is unknown, but can be another problem cause. One a Dell 2412 or 2312 it can lead to a exagaration of those colors, making it look not very nice.
As long as the monitor is profiled and calibrated, is it not Lightrooms job to make appearances optimal within the limitations of the display (i.e. "soft-clipping")?
If you profile your camera with ColorCheckerPassport, it can lead to relatively high levels of saturation, depending on the objects you photograph, like flowers, foliages (many shades of green, some quite saturated), or man-made stuff like make-up, clothing.
Whether these levels of staturation are correct is not the issue here, but can add to a wrong display on your monitor of those saturated colors.
I am not going for "natural" here (see attachements). So what you are saying is that very saturated images are more troubled by color management inaccuracies?
Personally in cases where i worked with dual-monitor setups, i Always found one monitor to suffer from the other, unless both were identical in model and type.
I have one "good" and one "bad". The bad one is used for increased real estate and for having an sRGB-calibrated point of view.