Tag Toolbar and labels of Gmail

I've received many questions about synchronizing tags of Thunderbird and labels of Gmail. So, I write answer for the questions here.

In order to synchronize Thunderbird and Gmail, you should use IMAP. On the Gmail's IMAP, labels of Gmail are converted to Folders then Gmail passes them to Thunderbird. When you move a message to a folder on Thunderbird, a label of a message is changed on Gmail; when you change a label of a message, a folder in which the message is stored is changed on Thunderbird. See the help for detail.

Namely, in other words, Gmail's labels are equivalent to Thunderbird's folders, not tags. Since it is a spec of Gmail, it is difficult to change the behavior or recognize a Gmail's label as a Thunderbird's tag. I think it is very useful if Gmail's label could be regarded as Thunderbird's tag, too. But I have no idea for Tag Toolbar to realize the request.

Anyway, Google, Mozilla and MailCo would know the issue, I think. Some solutions might be proposed by them. And if you have any good ideas, please tell me.