As the one who gave a thumbs down at the idea of teabags... I will openly confess I did so simply because it "sounds" like a bad idea to me... I do not "know" of any reason not to try it and I do not have any personal experience suggesting it's a bad idea...
The type of tea may also make a difference... some teas have stimulants (caffeine) while others have mild sedatives (sleepy time teas)... Also any array of different herbs with mild effects can be found in teas...
These are the reasons it "sounds" like a bad idea to me... but personal experience tends to override logical speculation... so although I would use one of the other methods suggested, I will remove my thumbs down on the idea