Serving the PF Hierarchy
An Office 365 tenant can support up to 1,000 public folder mailboxes, but only 100 of the mailboxes can serve the public folder hierarchy to clients. Each of those mailboxes can support connections from up to 2,000 active users, meaning that the maximum supported connected population is 200,000 users. This is enough for most organizations but might become an issue in the largest Office 365 tenants.
Exchange Online Reduces the Load
When Outlook desktop connects to Exchange, AutoDiscover returns a list of resources to which the mailbox can connect. Among these resources is a public folder mailbox (see below)

Controlled Connections
A recent change in Exchange Online allows you to reduce the overall load on public folders, you can do so by removing public folders from the view of mailboxes that don’t need to access them. This can be controlled at an organizational or mailbox level.
By default, every mailbox in a tenant can access public folders, so the PublicFolderShowClientControl setting in the organization configuration is $False. In other words, you’re not interested in controlling public folder access on a per-mailbox level. If you update the configuration and change the setting to $True, AutoDiscover checks the PublicFolderClientAccess setting for the mailbox to know if it should include public folder information in the data returned to Outlook. If the setting is $True, AutoDiscover returns public folder information. If $False, it does not.
To change the setting for a mailbox, run the Set-CASMailbox cmdlet. For example:
Set-CASMailbox -Identity James.Ryan -PublicFolderClientAccess $True
To set the organization configuration, run the Set-OrganizationConfig cmdlet. For example:
Set-OrganizationConfig -PublicFolderShowClientControl $True
After changing the setting, it takes a little time for cached information to clear and the new setting to be effective. You should expect to see public folders appear or disappear (depending on the setting) from Outlook within an hour of an update. Because these settings control how AutoDiscover behaves, it is not dependent on any specific version of Outlook. However, the settings do not affect OWA as it does not use AutoDiscover to retrieve resource information.
The default value for PublicFolderClientAccess is $False, so it is not a good idea to update the organization configuration and set PublicFolderShowClientControl to $True unless you first update the mailboxes that you want to continue accessing public folders. For instance, you might decide that only users in the U.K. should use public folders, you can run some PowerShell to find those mailboxes and update the setting. For instance:
Get-ExoMailbox -RecipientTypeDetails UserMailbox -Filter {UsageLocation -eq "United Kingdom"} | Set-CASMailbox -PublicFolderClientAccess $True
Microsoft has not said yet if this change will be ported to Exchange 2016 or Exchange 2019. I expect it to be, but you never know. Their official post about this topic doesn’t mention this point.
Public folders have a home in Chapter 8 of the companion volume for the Office 365 for IT Pros eBook. We bundle the companion volume with the main book if you buy from Gumroad.com, but you have to buy it separately for Kindle.