It depends. Older computers usually guzzle power, especially if you look at the absolutely awful Pentium4 systems. You're probably better off getting a RasPi or something, depending on what exactly you're trying to do. Newer systems have gotten much better with energy efficiency, so they'll pay for themselves quickly through lower electricity bills.
>TVs with higher resolutions might come out, but lower resolution ones continue to be sold new (implying demand exists at some price)
We're already seeing a limit here. 8k TVs are here now, but not very popular. There's almost no media in that resolution, and people can't tell the difference from 4k.
For a while, this wasn't the case: people were upgrading from 480 to 720 to 1080 and now to 4k.
>and then why should anybody want to replace a functioning old TV with a newer one of the same resolution?
They probably don't; if they're upgrading, they're getting a higher resolution (lots of 1080 screens still out there), or they're getting a bigger screen. It's possible they might want newer smart TV features too: older sets probably have support dropped and don't support the latest streaming services, though usually you can just get an add-on device that plugs into the HDMI port so this is probably less of a factor.