I would be interested to know if there are any free alternatives to g-suite/custom domain email. I'm not sure what Inbox was, but I've been using gmail/g-suite for many years without any real issues. I'm only using it because it's been free, however the free edition is no longer available to new signups. I've been recommending FastMail or Office 365 depending on who's asking me for advice, and I really would like to have a free option as many people I talk to are non-profit, charity, or simply resource limited.