Tim has a point - but perhaps it's a bit exaggerated. I have Michael's photo from inside the Rococo church up on my secondary display as I write this - both displays are properly calibrated and profiled. It's actually a good choice of a photo for the context of this discussion, precisely because it has such a large and difficult tonal range to deal with. I don't know how the original raw file (if there was one out of the camera) looked, nor do I know how much editing Michael did with it to produce this JPEG. It's a printable resolution (180 PPI - the lower limit I would print) but has about 4700x3100 pixel dimensions, so resizing it to 360 PPI without resampling would allow me to make a very decent (resolution point of view) 13 x 8.6 inch print. So Tim is correct that the resolution is adequate for at least discussing this photo. But reverting to the main point about the tone mapping and how to make it print so that it will look good on paper, I've prepared a series of exercises in Lightroom 7.1 which I think gets to the heart of screen versus print and what paper suits what kind of photo. There are 8 screen grabs and we are allowed only 4 per post, so this spreads over two posts.
Screen grab 1 shows the photo on display without softproofing. As Tim observed, there is some blocking-up of shadow detail, as confirmed by the bunching up at the left side of the histogram. But I know from experience that this shadow detail could be further revealed if one wanted to do so. I also know from experience that this kind of photo should be printed on a gloss/luster medium because of its shiny appearance and wide tonal range. So screen grab 2 shows it under softproof for Ilford Gold Fibre Silk (IGFS) in an Epson SC-P5000 (the largest gamut inkjet printer on the market along with its larger-format siblings). You will notice there is very little difference of appearance between illustrations (1) and (2), meaning that with the right printer/paper combination you could be about equally satisfied with the tonal depth seeing it in a print or on display with no softproofing. However if I repeat the same softproofing exercise but this time using the profile for a high quality matte paper (e.g. Canon Premium Fine Art Smooth) having respectable gamut for a matte paper, I could be disappointed because the dark tones would come out on paper rather muddier than suits the photo (Screen grab 3). So the moral of the story thus far: if you are going to print this, don't make a matte print and then complain that it lacks the tonal range of what you see on a non-softproof display version; use something like IGFS. Or do specific matte-based edits under softproof that make the best of a disadvantaged situation from the point of view of tonal range. That can get you a good part of the way to bridge the difference between matte and glossy, but not all the way. (And for all those who pooh-pooh the usefulness of softproofing, this demonstration might get you to think otherwise about this important procedure.)
So let us turn to some "playing around". In the IGFS softproof version, my top-level analysis of how it could be improved (to my taste) would be to tame the highlights a bit and open the shadows some. I did this to the IGFS softproof as seen in screen grab 4. You can see the adjustments in the menus to the far right. I still thought the shadow detail at the very bottom of the photo could be brought out more, so I used the graduated filter to further open that dark area (screen grab 5). The "final" photo is in screen grab 6. By the way, I really do like corrected perspectives, so I used Lightroom's superb Upright controls to get the verticals right (screen grab 7). Now before we leave this version, there remains a question in my mind about whether the colour balance is right. Is the interior of the church really that blue, or is this a case of the camera sensor seeing dark areas "blueishly" as they often do, but when we are in the scene our brains adjust to not be seeing blue. I could easily rebalance these colours by clicking the white balance eyedropper on a suitably blue area and the photo's whole colour scheme changes dramatically, but not knowing the scene appearance I won't bother with that here.
Turning to the question of matte paper for this photo, I created a proof copy in Lightroom of screen grab 7 and changed the softproof profile to Canon Premium Fine Art Smooth. Then I set about to converge its appearance as closely as I could to that of the IGFS softproof. The strategy is to increase contrast in the darker tones by upping the lower-mid tone brightness and lowering the deep shadow tone brightness, then increasing clarity which further separates at a micro-contrast level between the various darker tones in the lower part of the tone scale. Finally, I applied a graduated filter to the highlight area at the top of the photo and dialed back both the highlights and Clarity a bit to appropriately counteract the slight exaggeration of the highlights from the immediately previous adjustments. The end result for matte (screen grab 8) is snappier relative to where we started, but I would still prefer this particular photo on IGFS, and if it were printed on matte I would agree with the OP that the screen view is more satisfying than the print view. However, printed on IGFS, I would not agree with the OP's basic premise that prints can't match the screen for tonal range. So as usual, a profound conclusion here: "it all depends............." and perhaps some deep ends too. It depends on the photo, it depends on the paper/printer combination, it depends on how well you know how to edit the photos for optimum appearance on the chosen media, etc. I could have taken this further, but an hour later, and we see the main points - at least to me - at issue in this discussion.