See what I mean
Wrong L-Points... you're referring to the Earth-Moon L-Points, which are just 384400 km away from Earth, 60 degrees ahead and behind the Moon in its orbit.
However STEREO is investigating the Earth-Sun L-Points which are 1 AU away, 60 degrees ahead and behind the Earth in its orbit around the Sun. Anything orbitting around them would potentially be lost in the Zodiacal Glow, and further around the orbit, closer they get from Earth's point-of-view to the Sun.