Eventually people will miss various defects because of nostalgia. Like the Vectrex buzz, I'm sure to some people that's what they want to hear in the background as that's what they remember it sounding like.

Many old games were programmed to take advantage of the flaws with composite input, like dithering blending together colours and using similar effects for transparencies, shadows, or other techniques. The games will still play on other displays or with much improved video output, but you might end up missing some intended details. Much like looking at the original Mona Lisa and seeing the brush strokes and layers of paint, compared to a poster print of the Mona Lisa sold in the gift shop. Eventually there might not be a way around it as original hardware will all fail eventually. Like old LCD displays starting to separate between layers and leak. It'll all be gone eventually.

Personally I will avoid getting an OLED TV at all costs. Those are highly susceptible to burn in and the whites turn yellow in very little time, my phone has an OLED display and while I watch internet videos on it for convenience the display quality is now pretty weak with plenty of burn in and inaccurate colours. It conserves battery life which is good for a phone but for a home monitor I'm not concerned about that level of energy reduction.