Outlook Cached Mode offloads IOPs from the server to the workstation, provides offline access and also makes the user experience less vulnerable to unreliable or high-latency internet connections. So Cached Mode is recommended for Exchange Online and is the the preferred mode to connect Outlook with Exchange.
Unfortunately there are some scenario's where you can't enable Cached Mode, for instance stateless (VDI) desktops or RDS/TS hosts when customers for some reason are not able to store the .OST file on a fileserver.
So far nothing new for you as an experience Exchange admin. But did you know that you can specify per-mailbox if it's allowed to access with Outlook in Online Mode? This can be controlled with the Set-CASMailbox cmdlet. This cmdlet is available in both Exchange 2010 and 2013, however the switch to allow Online Mode is not available in Exchange Online.
It's very easy to block access with Outlook in Online Mode for a single mailbox:
Get-Mailbox <user> | Set-CASMailbox -MAPIBlockOutlookNonCachedMode:$true
A value of True enables the blocking of Online Mode clients, set the value to False to disable checking of the connection mode. False is the default value.
The user experience is not that great, a rather generic error message is displayed when the user tries to connect in Online Mode:
So if you have the requirement to block Outlook in Online Mode, you can do this with the Set-CASMailbox and the MAPIBlockOutlookNonCachedMode switch.
Beware though, setting MAPIBlockOutlookNonCachedMode to $true breaks New-MailboxExportRequest which means you can't export the content from this mailboxes to PST. Not something you would do every day, but good to know.