"All in one" is not an easy match to IMAP, which most users appear to find to be more useful, given that many of us want to see our email on more than one device.

If you have been using the alternative, POP, and are happy with it, then yes, you can set all your accounts to use it, and set them in Thunderbird to share a common Inbox, the so-called Global Inbox under Local Folders. You can individually set certain folders, such as Sent and Trash, to use a designated common location.

An alternative is to use the built-in Unified Folders view mode, which constructs a set of virtual folders which are composites of the real folders. So you'd see an Inbox which delivers the contents of all your Inboxes, and so on for Sent, Trash, Junk etc. Its main shortcoming, IMHO, is that since it can only amalgamate folders which are common to all accounts, it can't do anything useful with user-defined folders, so you end up moving between Unified and other folder views. If you do like the look of Unified Folders, it may pay to install the Folder View Switcher addon to facilitate changing between views.

My own method is to use several Saved Search folders, which are user-defined composite folders, so these can combine disparate folders. I use these for Unread Messages (anywhere), Recent Messages (in selected work-related folders), project-related folders (across current and archived folders) and so on. It also lets me collect Junk, Spam and Bulk Mail folders into one, simplifying my triage and reporting of UCE.

Thunderbird doesn't use a pst file (that's proprietary Microsoft design) so that's not a feature that can be compared. But the mode of storage shouldn't and needn't be of concern with the presentation and aesthetics aspect of working with email. Thunderbird uses mailbox format files, one per email folder, and along with your address books, add-ons, filters, themes, layout customizations, these are known collectively as your profile. You can use multiple profiles if that suits you, but IMHO multiple profiles are overkill for the vast majority of users.

Thunderbird is vastly superior to Outlook if you are interested in message headers, full message source or working directly with HTML mark-up. Not to mention the wealth of free add-ons available for Thunderbird, allowing you to customise it extensively.