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The comparison between CRT and digital is not as simple as "625 vs 4k". Those analog signals were intended for a triangular subpixel shadow mask with no concept of horizontal pixel count, making them effectively into ∞×625i@50fps signals (1), compared to the digital fixed 3840×2160@60fps square pixels regardless of subpixel arrangement.
It takes about a 6x6 square pixel block to correctly represent a triangular subpixel mask, making 4K LCDs about the minimum required to properly view those 625i@50fps signals.
(1) I'm aware of optics limitations, CoC, quantum effects, and ground TV carrier band limitations, but still.