This is how the Great Library works. Our tech tree is not false, the GL becomes obsolete when Education is discovered, but as our tech tree shows us, we have not discovered it yet. But I doubt that we'll get Military Tradition or Free Artistry out of it. 2 Civs getting FA for example would mean that 2 Civs have education which would mean that we would already have got it free making the Great Library obosolete before we could get FA. MT is more of a possibility but I doubt that they'll research that far before another Civ researches or trades for Education again giving us Education for free and making the Great Library obsolete. This tech, Education, is likely to be only tech we'll get free.
Of course there really is an exploit here (that I do NOT propose we use) and that is to give your Great Library city to another Civ, preferably much weaker just before you get Education. You surround the city so they can not bring in large numbers of defenders, then when large numbers of techs have been discovered retake the city and get all the techs that 2 Civs have (which can take you to FA, MT and even into the next age) plus of course Education. In the meantime you save lots of gold.
In short, stop research for now until we get Education for free then continue on the already decided route to Democracy.