Yeah it broke my use case. I used to run `curl --retry 9999 http://1.1.1.1` and since it didn't exit, the heat generated by the running curl process kept me warm in the winter. But now http://1.1.1.1 returns immediately, so I'm freezing!
I mean, for smaller routers that had static routes set for that subnet, it would probably just keep working - the issue being that trying to get to real addresses in the 1.0.0.0/8 network (or parts of it) wouldn't work.
If you were BGP peering then you'd probably get a real route into your local table though.
So yeah, some stuff would probably have just broken, but that's the risk you take using parts of the IP space you shouldn't be using!
To be honest I feel as bad for them as I do for Hamachi, when their (otherwise quite nice in that it was a spiritual predecessor to Tailscale!) overlay VPN service fell apart once 5.0.0.0/24 became publicly assigned.
(not worried about them, just curious)