Hey Email looks to have some great features, but at $12/user/month it's more expensive than Exchange Online or Google Workspace, which means it's more a choice about whether a user values Hey's nifty features (and they do look nifty) than an easy option for email domain hosting vs the OP's issues with iCloud+.
For my family's email needs, $12/user/month is a bit of a non-starter given the competition.