It's not "hardcoded into the game".
See: Emulators
Old games are set to their original resolution when played on new systems because - shocker! They look best in their original, intended resolution!
All you get from upping the resolution of old games is a lot more clarity on the horribly low-poly models and horribad textures which are normally covered up nicely by the low resolution.
Nope. You are completely wrong.
Games look far better in high resolutions. Game companies are just too lazy to do so with backwards compatibility. Note how the games they release on things like PSN/XBLA are upscaled since people pay for them.
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