Our TV just went kaput (after 11 years, thank you for your service) and there's no way I'm getting an Internet-connected TV because I'm already worried enough about my blood pressure. There don't seem to be many consumer options, but is there some reason why we shouldn't just get a commercial display intended for digital signage, like this one?

https://www.cdw.com/product/tcl-te65n-ten-series-65-led-backlit-lcd-display-4k-for-digital-signa/8463458

TCL TE65N TEN Series - 65" LED-backlit LCD display - 4K - for digital signage - TE65N - Large Format Displays - CDW.com

Buy a TCL TE65N TEN Series - 65" LED-backlit LCD display - 4K - for digital signage at CDW.com

CDW.com
@mogwai_poet I've got an LG G3 smart TV and it's quite happy to be a dumb monitor for my Apple TV. The TV itself has never had an internet connection and works wonderfully, so if you can find one of those you're good. If you want to avoid consumer TVs entirely a big computer monitor is your best bet I reckon.
@mogwai_poet Also as others mentioned you will need some way of switching inputs & providing speakers if you decide to avoid a smart TV. An AV receiver is best but that's extra money. Make sure whatever screen you buy comes with a remote or can wake on an HDMI signal.