As a nomad, and someone who does run a self hosted mail server for fun, I don't think that's such a good idea. As mentioned, phones can be stolen or broken or just off. Do I want to increase dependencies on phone further by it being the primary store for all my mails as well? Each platform, which is not using TOTP MFA would still depend on email OTPs and so with a broken phone one completely loses access. With TOTPs atleast I get to save a few recovery codes. The cost of losing a phone would mean losing all that data as well. Now, one could say we could and should keep backups. Then, comes the cost of losing access to new mails while the phone is incapicitated. Then, even setting up of email server on a phone with dynamic IP is a whole can of worms in itself and let's go with the easiest solution of using a VPN. So, now we need a VPN, a backup solution and a device to quickly accept emails when the primary device is down. Aren't we just building remote mail servers now? I do have a cloud instance serving my own email but do we expect most users to handle the infra? So now for making it easier for everyone and amortizing the costs let's start offering a solution where multiple people can run email accounts in a single server. Now we have gmail and other providers.