That being said, coffee is essential in the morning for low blood pressure people. Tea doesn't quite start the engine up the same way - clearing and waking up the brain is no use if the heart is still at 50 bpm and the eyelids are as heavy as the Iron Curtain.
Does such a thing exist? Usually "tea" is made from tea leaves and other similar drinks are called "infusions" or "herbal tea" instead. I have never heard of decaff tea, but maybe it is common in other places?
You're right that drinks not brewed from camelia sinensis leaves should technically be called an infusion or tisane. That includes fruit "tea" and infusions like rooibos, chamomile, nettle, or maté. However it's very common even in the UK to say "fruit tea" or "chamomile tea".
You're 'avin a laugh sunshine.
Walk down the tea aisle in any British supermarket and tell me the radio of decaff's to unmolested teas that you see!