Hi Peter,
As you know, Cached Exchange Mode provides you with a better experience when you use a Microsoft Exchange account. A copy of your mailbox is stored on your computer. This copy provides quick access to your data and is frequently updated with the mail server. Therefore, if your mailbox storage is large (for example, more than 2 GB), we recommend you enable the Cached Exchange Mode, it will reduce the time that Outlook client synchronizes data from Exchange Online. And it also allows you to access more emails when you are offline.
You can archive old emails to release available storage of your Office 365 mailbox. And in Office 365 we have default retention policy to help users move old emails to archive mailbox. You can also set up personal and customize retention policy or move old emails manually. The detailed information for your reference: Retention Policies in Exchange Online
Thanks,
Bourne Zhang