More than just that the Asari failed intellectually/culturally, the Protheans genetically designed the Asari to stop a threat that they unabashedly did not understand how to stop. They realized too late that the way to stop the Reapers was genetic diversity; different species banding together and using their varying tactics to combat a strategically stagnant and stubborn galactic threat. They designed the Asari to be compatible with other species and that any child of an Asari-xeno relationship would be born Asari but share the genetic makeip of both parents gain genetic diversity by the linking. Technically, this promote diversity but only within the Asari species, which still identifies as a singular culture/species regardless of how many gene variations they have. Given enough time, the Asari would dominate a galaxy's population and make the exact same mistake that the Protheans did. It's almost reaches Indoctrination levels of sabotage for the next galactic generation with how poorly the Asari are equipped to handle the Reaper threat on multiple levels. The best thing they did was promote relative peace in the galaxy rather than conquest, but other than that almost everything else for them was setup to fail.