You’re thinking of spatial aliasing, which can be improved by sitting further away from the screen. The problem here is temporal aliasing, which has more to do with the resolution and size of the display, and is not improved by sitting further away.

Temporal aliasing gets worse the larger individual pixels are and the lower the pixel density is, which is why it will more negatively affect the TV viewer even if they appropriately match TV size and distance.

And then you also have to consider the fact that they don’t make 1080p or 1440p for that matter TVs at the size you’d need to view from the average livingroom distance. So playing a game at 1080P means your TV has to scale that 1080p across its native resolution which will result in a blurry picture.

Here’s a video that discusses the issue