Outlook on the Web is lacking a lot of features
Outlook on the web lacks basic features and some design choices offer inconvenience rather than benefits. These points are at the User level.
Users do not have flexibility to choose what gets deleted while using the clean up mailbox option. The options for the selected folder are "All" "3/6/12 months or older". There is no option select specific email address to delete or specify only emails with attachments (with choosing attachment size range) to get deleted.
There is no easy way to search for specific emails, select them all and delete them. Look at the example for clarification:
User A searches for B@domain.com emails in all folders. Search results show 100 emails. User A clicks the checkbox next to "All Folders" but it only selects the visible emails on screen. User A checks the "select everything" option but it doesn't find it, it needs to hold shift to include further emails into the selection or zoom out the browser screen so that the checkbox selects everything. User A deletes the 100 selected emails and goes to the Deleted Folder to confirm deletion. User A searches for B@domain.com emails to confirm everything is deleted. User A finds out there are still emails left for B@domain.com. The search results is limited and shows you results in a series of pages that do not update unless you input another search query.
Inbox Rules only apply to future emails and not to past emails so they can't be used for organizing and cleanup of old emails.
Emails that are read from the search results are not marked as read after returning to the inbox. There only read if the user right clicks and mark them as read. I don't understand why this is by design. Normal behavior should be applied to the search results.
As an Admin I would like users or some users have the ability to manage their own inbox and storage how they want without having to resort back to the admin center. As I come to understanding most of the features are present in the Outlook desktop application but there are no plans offered from Microsoft that give access to only Outlook.