Great library is a trap like pocket kings in a texas hold-em deal. It looks great and makes you bet everything on it, but so much beats it, and the actual chance you can do anything with it is low, so you're hurting yourself more than helping.
Only build great library for 2 reasons: if you can get it done VERY quickly, as in egypt with marble quickly, or if it will springboard your military, like for rome or iroquois for iron working.
Otherwise you're actually slowing yourself down, spending the production, when a normal library + granary early nets the "same thing".
"But I get a free tech and tourism slots!"
The free tech isn't worth sacrificing earlier infrastructure, and by the time stacked tourism bonuses even matter (modern age and beyond) you'd still have done more, faster with earlier infrastructure.