First, IMAP is not something Thunderbird can change: IMAP has a specific, rigid, structure, as does POP. What thunderbird does is use it as designed. I wish you well in finding an email client that treats IMAP as thought it was POP. Second, you are unclear on your intent. If it is to have all messages appear as one, that is available if using Unified Folders setting. Third, you have not explained what you are doing in moving messages to local folders. Details are helpful. Thank you.

Unified folders does not work with IMAP. You could write software to treat IMAP just like POP3. I now have to use "Message Filters" to move all of my email from all of my different email accounts into the Local Folders. And, it is inconsistent. Sometimes it works...sometimes it does not. And now, Thunderbird fails to identify anything I have marked as JUNK and move it to the JUNK folder. IS THIS NOT CLEAR???

Well, unified folders work very well with IMAP. I have three IMAP accounts and it works great. No, there is no need for Mozilla to make IMAP work like POP. If people want POP, they should use accounts that allow POP and not put the onus on the email client. Possibly, if you share screenshot of one of your message filters, we can help. What you're wanting to do seems straightforward. To clarify, a unified folder is only a view, not the actual move of messages to a single folder. I think, with example of your filter, we can help you resolve your concern.

Well...I just checked unified folders and it made a complete mess. It's still showing each individual email account, not once, but twice...

Here's a picture of my mess...

Ok. I deselected "All folders" view but things are still a mess...see attached screen shot...