Did you replace it with a “dumb” phone for emergencies?

No. For emergencies have had to rely on nearby human beings, like the 1990's.

Any crazy stories from this?

Many but I like to save them for real life.

One tamer one is the time I stopped to help a woman whose car broke down on the side of Route 5 near Camp Pendleton. Her phone had died and she was stuck there waiting for help. I didn't have a phone, but knew there was a Marine Base nearby so drove there to get help. Unfortunately it was dark and I went down the wrong road and suddenly see a Marine running after my car with an M-16. Luckily he didn't shoot, laughed at my Hawaii Driver's License, and directed me to a nearby gas station, where we were able to phone for help.

Not having a phone makes every day an adventure! :)

I have dreamed of ditching the phone but haven't because so many sites that require a phone number to make an account, and some that use that number to validate your identity. How do you get around this?

Google Voice. Without Google Voice it would be near impossible (maybe there are some other good VOIP solutions but not sure).

You definitely do need a phone # for accounts and auths.