I'm scared that if the pi is down then the whole internet is down (i'm not always home with my family, so if I'm away I couldn't fix it).
How do you manage failover ?
Even so, normally you can set a fallback DNS server on your router, and you could have two little Pi Zeros on a plugstrip in a closet somewhere! (Or just set the fallback at opendns or something)
One option would be to set up two Pis, and distribute both IPs in DHCP. If one is down, or can't resolve, clients will fall back to the other one. The chance of both being down at once (unless it's something that takes your network down) seems low, and the cost of a Pi Zero W (~$10) wouldn't add much.