Without going too deep into the tech aspect of this, modern displays (pretty much all flat screen TVs made in this century) require an input signal of 480p or better from your video game console, because they were not designed with old gaming consoles (anything before 6th gen) in mind.

Something as simple as a Retrotink 2x can make a world of difference. No need to modify your old console, just hook it up to the Retrotink’s composite or s-video input and play on your modern TV. Decent picture quality and almost no input lag.