That's funny since most printed text is printed at like 72dpi and nobody complains that printed text is pixelated or "unclear." The human eye isn't that good. What you are loving isn't resolution related -- it's the better backlight giving you better blacks than what you had on old 1080 monitors.
Uh, no, you're thinking of PPI on displays. Even cheap printers can usually handle at least 300x300 DPI. Most laser printers I've seen default to 600x600, and even ones marketed for home use are often capable of at least 1200 in at least one dimension. Many inkjets also are able to increase their DPI for "high quality" or photo printing.
Let's take an average computer monitor, however--say a 22" monitor with 1680x1050 resolution. This gives about 90 PPI (or DPI as it's more often called here, even though some would argue that is not the correct term for displays). Early computer displays were often about 72 PPI, which is where your figure comes from (though Microsoft used 96 DPI for reasons beyond the scope of my explanation). Now, Apple's "Retina" and other high-DPI displays are on the market for both desktops and mobile devices, with PPI often in the 200s or 300s--closer to print.
The difference people perceive is most certainly related to pixel density and not to better backlighting. While a better backlight might help with increasing contrast, if you compare high-DPI vs. "regular" displays side-by-side, I think you'll find the difference clear--as if this even needs to be explained given that your description of printed text is egregiously incorrect. (For added fun, turn off font smoothing and compare--half the reason people think text looks decent at all on a 90-ish DPI monitor is font smoothing, usually in the form of subpixel rendering on LCDs.)