The worst occasion I've ever had was the one time I was traveling. I was getting by with only wifi and, naturally, didn't have a phone number to confirm my account with. I didn't have a number bound to my account, either, making the whole process pointless.
How did I get into my account? I asked a random guy who walked by if I could login to my email on his phone (since at that point I'd left my wifi area and couldn't login with my own device). It was essential that I check an email at that point, so I didn't have a choice. It was anti-security--I literally gave full access to my email account to some man I never met before in a different country.
Google needs to stop pretending it's some security measure. It's not. It's data harvesting, plain and simple. I just wish they'd admit it.