Pixel art was MADE to be viewed on a CRT TV. The blooming, scanlines, etc are part of the image that smooths it out, blends colors together, and gets rid of the harsh edges.
The original game artists created everything with that analog distortion in mind, so the raw pixels aren't necessarily what they intended you to see.
Don't get me wrong, raw pixels can look cool too! And if you like that look, then by all means go for it.
But it's worth trying a nice CRT shader on them to see if you might like it even better!