Instead of using a free email service provider you can register your own domain name.
In addition to having an email service that's portable across different email service providers, paid hosting comes with tech support and email addresses that can't be permanently lost.
I have, in the recent past, created a hotmail account without a phone number, but when I tried logging into my account from another location (ie at work), it forced me to verify my phone number, otherwise, it wouldnt log me in.