How to make Thunderbird play nice with Google mail

There is no need for a workaround anymore. Thunderbird version 38 and newer support GMail labels. According to the documentation an e-mail is downloaded only once:

Note that a message can have multiple labels (for instance, "Personal", "Travel", "All Mail" and "Starred"). In this case, a single copy of this message will be downloaded, but it will be displayed in all the corresponding Thunderbird folders.

For the record, IMAP does support tags (they're called keywords and implemented as flags), and Mozilla Thunderbird and SeaMonkey use IMAP tags.

See this discussion from 2006 with Mark Crispin.