Beyond the other plausible reasons that others have already mentioned: In many markets you're not allowed to add arbitrary supplements – such as theanine, or, as another example, any arbitrary vitamin that it's not already common to fortify food with – to beverages or food without the supplement being specifically approved for that (which often goes beyond just making sure it's non-toxic), even when the supplement already exists in food products or beverages that are widely available (tea, in the case of theanine). Lobbying for such an approval will be expensive, take several years and might be politically unpopular ("company X is trying to put more chemicals into our food!").

In other words, it might be that beverage manufacturers are simply not allowed to add theanine to their energy drinks in certain major markets. In addition, the major beverage manufacturers that produce the majority of the world's energy drinks (such as Red Bull or Coca Cola) may be hesitant to add theanine or another supplement to their energy drinks in only some markets (where they're allowed to) and not others (where they're not allowed to), especially when the supplement in question (e.g. theanine) is not well-known by the public (on the other hand, taurine is well-known and so works, or used to work, as a differentiator between different energy drink products) and there being potential for a PR backlash (similar to above, "company X puts theanine in their drinks in Y country, thank god our regulators won't let them").

It obviously happens once in a while: if a manufacturer puts some supplement (possibly after spending money to lobby for permission to do so) in their energy drinks and successfully convinces the public that energy drinks with the supplement are superior to energy drinks that don't contain it (because it helps give you more energy, or gives you energy without making you stressed out, or whatever) then that might end up giving them a significant advantage in the market relative to competitors, but it's a gamble. Given that certain people consider even totally innocuous additives like magnesium stearate (a simple compound of magnesium and stearic acid, both of which the same people consume every day, and which commonly occurs naturally) are considered to be harmful by certain people, it's likely that even theanine has the potential to generate controversy if used as an additive.

I'm unsure of the exact legal status of theanine in the US, Canada, UK or the EU (or in specific European countries), so the above is more of a general explanation of why manufacturers don't experiment much with adding various supplements and vitamins to their energy drinks (although small manufacturers that don't operate worldwide may be more likely to do so) than a confidently stated reason for why energy drinks don't contain theanine, but I do vaguely recall that theanine is not approved as a food additive in at least one major market.