2 factor authentication won't turn off- alternative options??

I know this has been asked before and the answer is simply ' you can't turn it off on newer versions of iOS'. However, what am I supposed to do since my iPhone is broken and won't turn on, so I can only verify my iCloud mail via my laptop. This is so impractical as I cannot carry my MacBook with me everywhere and every time I want to access my email. I know you can start a new apple id, but I have so many details etc connected to the account. I think Apple shouldn't be encouraging people to do two-factor, because although secure, it is a completely impractical feature in circumstances such as lost of broken phone, especially when you are abroad and don't have access to your 'trusted number' for verification. Please help!