It's a good idea to replace older calls to the Get-Mailbox cmdlet with Get-ExoMailbox. However, it's not just a matter of cut and paste updates.
Many Exchange Online scripts use the old Get-Mailbox cmdlet to fetch mailbox data. It's time to change these calls out and replace them with Get-ExoMailbox. The new cmdlet is faster than the old and more resilient in its ability to handle server glitches. There's no reason to continue using the old Remote PowerShell cmdlets unless you like slowness and errors.