It's different in a thumbnail compared to at high resolutions, although giving the benefit of the doubt I presume you checked it at full screen resolution/maximum 4K video detail, ideally on a high resolution display (just mentioning this in case you didn't or for anyone else who didn't). Those games were never meant to look pixelated, and the 320 x 224 backgrounds just do not survive being scaled up to modern HD resolutions, regardless of whether you do a nearest neighbor approach (too pixelated) look or a filtered look (too blurry/smooth). They need some sort of additional "CRT-esque" treatment to look right, and even then they still lean towards blurry, but well... that's the nature of the original asset size. The PC version with the Moguri mod exists for people who want sharpness/clarity on modern HD resolutions and don't mind the drawbacks of that approach.
You do, however, bring up one good point about the obvious drawback of scanlines and some of those filtered approaches. That is, they dull the image because less of the overall scene is bright (due to more of it being scanlines). This is simply unavoidable to an extent because LCDs can't mimic a CRT. CRTs were "resolution flexible" in that they didn't have native resolutions, so they could show these low resolution assets at larger physical screen sizes without as much deterioration. Of course it would be as sharp as HD resolutions becasue we simply had HD resolution sharpness back then, but it'd be better than how those same HD resolutions show it now.
This is actually part of what made me like the way the "consumer 1 mode" looked, despite it not being as "accurate" to most CRT TVs of the time. It's a balance of a filtered/CRT look while retaining some vividness.
The best bet is to simply use a CRT, but that's not practical for most people. I think really high resolution displays (namely, 4K, and maybe 1440p, hence the disclaimer in that video) help here because these shaders/filters have more real estate to work with when trying to mimic scanlines and other stuff that would work on a sub-pixel level. OLED displays may also be better off here in retaining some of the brightness/vividness.
But at the end of the day... yeah, it's yet another example of why I'll cry "remake when, Square Enix, come on!" Capcom did it (Resident Evil 2). Even Konami did it (Silent Hill 2), and with a series they basically shifted to gambling machine duty. I'm keeping my eyes on Square Enix... it's their turn to do what those other two did!