Microsoft recommends maintaining a small foot print Exchange Server for managing mail related attributes, as these can't fully be managed solely from Office 365. This is because with directory synchronization the on premises directory is the source of authority for object attributes and these attributes must be managed from on premises.
When directory synchronization is enabled for a tenant and a user is
synchronized from on-premises, most of the attributes cannot be
managed from Exchange Online and must be managed from on-premises.
This is not due to the hybrid configuration, but it occurs because of
directory synchronization. In addition, even if you have directory
synchronization in place without running the Hybrid Configuration
Wizard, you still cannot manage most of the recipient tasks from the
cloud.
https://docs.microsoft.com/en-us/exchange/decommission-on-premises-exchange#why-you-may-not-want-to-decommission-exchange-servers-from-on-premises
Another reference for you:
Another key scenario where you are likely to need a Hybrid licence is
after you have completed your migration from Exchange Server 2010 to
Office 365. After moving your final mailboxes and if you have them,
Public Folders, you will decommission Exchange Server 2010. Most
organizations will keep Azure AD Connect in place after the migration
completes, which means Hybrid Identity (where AD remains the master)
is in place. You will therefore require require Exchange Server to
manage those attributes – and potentially to relay SMTP email, too.
This of course is a great use of an Exchange 2016 or higher server.
Finally – and it comes as a surprise to some organizations – if you
have never had Exchange within the organization then you might need to
install Exchange Hybrid servers for attribute management within the
local AD. As mentioned above – if you use Azure AD Connect, you will
have Hybrid identity in place. Many organizations running Domino today
and migrating to Office 365 find they need to install an Exchange
Hybrid server (or two) and utilize the free Hybrid licence.
https://practical365.com/exchange-server/how-to-licence-exchange-hybrid-servers/