What you're missing is that sometimes, the characteristics of a CRT are used for a visual effect that is completely missing on non-CRT displays.
For instance, it's arguable that a lot of low-res 16 bit sprites actually look better when on a technically inferior display because that's what the developers were using - and they would have drawn the sprites with the blur in mind. You remove the blur, and the sprites are a bit harder to look at [1]. (Take any of the SNES Squaresoft RPGs for a good example of this.) Scaliness were often used as a cheap method of texture blending.
A good description of this comes from here[2]: The chunky sprites with their often thick, cartoony outlines just weren't designed to be reproduced with sharp edges resulting from nearest-neighbor upscaling.
[1]: http://www.tested.com/tech/gaming/2982-a-link-to-the-past-ho...
[2]: http://cyber4education.blogspot.com/2010/12/crt-pixel-shader...
It's your system and you can play your games however you want, but it's not in question that many games were designed to be played on older displays.
And then you have modern games like the one posted here that aim to mimic those effects because they are now a style unto themselves. No need to denigrate it.
CRT contrast was markedly inferior at high spatial frequencies (as opposed to VESA contrast). The linked article is deliberately trying to simulate this. Even on aperture grille tubes this is obvious with pure white/black 50% ordered dither. This makes a big difference to legibility of text.
Brightness is lower than most LCDs, and fades quickly with age if it's set too high. Gamut is lower than high gamut LCDs, and color accuracy is similar to good LCDs.
Spatial resolution is much worse, especially as you can't benefit from sub pixel rendering. I've spent a lot of time tweaking CRT controls, and you can never get perfect focus and convergence across the whole screen. You can never get perfect geometry either, which is not an issue with LCDs.
Comparing a high end CRT to a high end image quality optimized LCD (eg. IPS or VA), viewing still images, from a normal desktop viewing position, I'm confident that the vast majority of viewers will prefer the LCD.
More importantly, LCDs buffer a least one frame. Many buffer 3-5 frames (!). This can be a serious problem playing for video games or other interactive uses if you need to rely on well under 100ms late4ncy. Rockband/GuitarHero is the canonical example of this problem, where they had to develop various types of adjustable latency compensation into the later games. Bad firmware can make this unpredictable, too; it is common for the firmware to select different algorithms based on the name of the input that you're using. (e.g. and LCD might buffer fewer frames if [[ $input_name =~ /game/ ]].
Once of the sources of multiple-frames of latency was the scaling/resampling stage that was needed to be compatible with non-native resolutions. Some of those algorithms are very slow. A friend of mine that makes FPGAs used in some LCDs has suggested that this slowness may be because the company making the monitor is too cheap to buy parts that were fast enough. That was a few years ago, though, so maybe these newer 144Hz monitors improved the situation.
For the same reason Quentin Tarantino is pouring much of his personal fortune into a movie theater that will run films in celluloid only. For the same reason vinyl is making a huge comeback. People think the shitty output is "richer", "warmer", and "more authentic"; and the better output is "cold" and "mechanical".
It's post hoc justification of nostalgia: people want to recreate the experience they had when they first saw a movie/listened to a record/played a game. They want the thrill back, or at least a reminder of it.
I'm guilty of this myself; when I run an xterm it's usually green (#7fff7f) on black or amber (#daa520, X11 color "goldenrod") on black, in a nice pixely font like Glass Tty VT220. Because I'm on a Unix system and want to feel the thrill of Unixing.
http://slack.net/~ant/old/ntsc-vs-palette/
It was also very common to assume there wou9ld be darkening from the scanline effect on arcade machines, leading to brightness problem in the emulation of some ames.
Nostalgia aside, CRTs didn't actually look that good originally. They weren't used for their visual effects, they were used because they were cheap and easy. Why would you actively make your content look shittier?
I suspect if you went back, and offered the people developing these games the option to play them on a modern display, without all the distortion and such, they'd much prefer it over the "CRT look".
At least, please, PLEASE let the player turn the effects off.