I don't know how you contrived to get multiple email accounts "under" Local Folders. You can get multiple POP-connected accounts to share the common Inbox in Local Folders. but ISTR they all merge into one and lose their individual identities. I wouldn't expect them to retain their separate names. (I don't use POP any more myself and I have no interest in merging accounts, so it's hard to attempt to replicate what you describe.)

Accounts added more recently will have been set as IMAP-connected by default, where possible, unless you intervened and forced them to use POP. IMAP-connected accounts can't share folders, though a similar appearance can be obtained via View|Folders|Unified

You may be able to set up new versions of IMAP-based accounts using POP instead and then you can set them to use Global Inbox too.

As it's difficult to visualize what you have there, can I suggest you post a screenshot. Use Paint or similar to blur or blot out your email addresses before posting.

I have just set up two accounts in a test profile using POP and set them to use Global Inbox, and indeed they vanish from sight. So that doesn't tally with your description. I think we need that screenshot to understand what you're trying to describe.

https://support.mozilla.org/en-US/kb/how-do-i-create-screenshot-my-problem