The light sensors in digital cameras capture high dynamic range images (tonal values that exceed the brightness range that can be printed on paper), at least if you're saving raw RGB files, and anyone with a Lightroom license and a recent MacBook Pro can process and display them. I'm sure there also are laptops for MS-Windows with HDR-capable displays; the magic number to look for is a brightness value of 1000 cd/㎡ (a.k.a. 1000 nits), although you can get at least a partial HDR effect with less, especially in a darkened room. You don't need an external HDR monitor.
The entertainment industry seems to be migrating to HDR for video, so it's no surprise that Adobe and Apple, in particular, are adapting their products to support this technique. All recent iPhones display HDR stills and video, and I gather that's true of much of the hardware for Android products as well. My understanding is that many newer consumer TV sets will display HDR content—although they also may require a dark environment. (I don't have any personal experience with Android phones or HDR-capable TVs.)
Unlike the traditional HDR technique that involves merging exposure brackets in order to squeeze the tonal values into a composite image that can be viewed on a conventional computer display or printed on paper, this newer HDR technique produces an image that is a much better representation of the tonal range that the human eye and brain can detect. The highlights can be much brighter and the shadows can include more detail. Depending on the subject, of course. An indoor photograph made under soft light won't look appreciably different as an HDR image than it would as an SDR image.
The reason you can't print this kind of HDR image is that you can't print highlights that are brighter than the surface of the photo paper. And when an HDR image is displayed on a conventional computer monitor, it's likely to look awful. However, it's possible to create a JPEG that will allow both conventional and HDR-capable monitors to display the same file properly by embedding a "gain map" in the file with the data needed by the latter. Lightroom supports this as an export option and it seems to work fairly well.