I never understood this.
720p texture doesn't mean anything, even "4K" texture doesn't mean anything, unless you're literally talking about a 4096x4096 texture.
I don't know where this idea comes from that mesh textures are directly related to display resolution, it's a lot more "complicated" than that, you can't talk about texture size as a universal thing.
It really depends on multiple things, like the camera distance from said texture is actually the most important thing. A texture that looks very blurry from close up in 4K, will look as bad in 1080p. A 512x512 texture can look super crisp on a mesh while a 4096x4096 texture can look blurry, depending on the UV map, on the scale of the object, how the texture is tiled etc... It really depends on the object, how it's used, how far you are from it, more than the display resolution itself.
And that's without even getting into material layers, normal maps etc which can make low resolution textures actually look really good.
A texture on a 3D object that looks perfectly clean from close up in 1080p should never look suddenly horrible in 4K.