Yes, there are problems with all studies, and it sure is fun to pile on, but a cursory search of examine.com confirms my own experience and that of amateur noot-ers: Theanine takes the edge off caffeine and helps focus. Caffeine+Theanine is the third highest recommended home treatment for focus (behind exercise and sleep) on r/nootropics for whatever that's worth.
You can find other studies here: https://examine.com/supplements/theanine/
I take it semi-regularly during times I'm over-consuming caffeine, but find that I come to resent its absence when I stop taking it.