Not a dumb question, really. The majority of displays available when HD got started were CRTs. The issue has to do with increasing the operating frequencies so that more lines can be drawn by the TV. As you note, your TV doesn't have any possibility of doing that. On the other hand, a customer from several years ago has a Sony G90 projector with a Faroudja line quadrupler that displays an incredibly film-like image, even when the Faroudja is being fed garden variety video. That has to do with the quadrupler figuring out what the likely pixels would be in between the bits of information that the regular video has, and then sending that signal to the display with a horizontal frequency, for instance, of something like 60 kHz instead of the older 15,750 Hz.