I host my own postfix server on FreeBSD and use the Evolution IMAP client on Linux. I haven't been in a situation where I need web access to mail in years so for me it's equivalent.

I started out about 6 months ago with this great guide:

https://www.c0ffee.net/blog/mail-server-guide/

The cost of a convenience like having a free email account is participating in the demise of the protocol-based networks that we have replaced with centralized products. There's many other great IMAP clients and maybe some of the features of Gmail/Inbox can be recreated using server side rules and scripts.