The only tool I know of is the ImportExportTools addon and this is folder based. The lack of tools should be telling you something about this not being common practice.

I don't see the attraction of a huge heap of individual eml files. What use could you make of them? How do you search them? How do you find the next message in a conversation?

I'd be thinking about copying out the mbox files, assuming that you're doing this as protection against a catastrophic failure and significant data loss. But one of the caveats for any backup is the ability to restore from it, and I don't see your individual eml files being useful for this. In truth, mbox files are hardly any better.

For backup and disaster recovery, rather than cherry-picking individual files, I'd be copying the entire profile. I know how to use a profile to restore Thunderbird. I'd be less confident about having its component data files and trying to stitch them back together.

I have figured it out. Once you setup IMAP on Thunderbird, you hold down CTRL and drag folders down to "Local Folders" in the directory tree. This gives you copies of the email files on your hard drive accessible to Thunderbird. Then you highlight groups of these Local Folders and Right Click and Choose Export All Messages-> In .eml Format. You then select a folder on your hard disk to put them into and what you get is the Original folder names with a subfolder labeled Messages and inside that folder are all of the .eml files. Then you can transfer them to USB or burn them to optical disc. My purpose is to save a plain english record of these emails in case I need a quick printout or read. Hope this helps the next user.