The difficult bit is making it not look like a screen. Even the fancy Sony "the frame" (which are supposed to do clever matching to room brightness etc) TVs don't get that quite right, and only do it in some special mode...

The costs in electricity bill is gonna be big compared to e-ink. Refresh rate of static picture can be terrible, OK for this use case. There's also color e-ink devices, though not many, and the colors were IMO too pastel-ish.

Although backlight of a second hand TV might also be dying, I agree say Chromecast on TV gives a nice effect. My oldest kid gets impressed, FWIW.

Good luck running that for years on a battery...