I had a customer ask if after they were done migrating all their mailboxes and services from their local on-premises Exchange Server to Exchange Online if they could remove their local Exchange server. You certainly cant blame them for wanting to with the recent news of zero-day vulnerabilities for Microsoft Exchange Server that are being actively exploited and that Exchange Online was not at risk.
I remembered a great article posted a few years back by Paul Cunningham on Practical365.com and in it the following:
“If you have directory synchronization in place, then you need to manage the mail attributes of users, groups, and contacts in the on-premises Active Directory, and then allow those changes to synchronize to Azure Active Directory. The only πππ½π½πΌπΏππ²π± way to manage the mail attributes on-premises is using the Exchange management tools, which requires at least one Exchange server to be running.”
The key word is πππ½π½πΌπΏππ²π± and sadly no new updates from Microsoft have come since 2017 so for now the answer is no you must keep at least one Exchange Server on-premises and this has been your #MicrosoftCloudQuickFix