I wonder how much info was just straight up lost this way.

It's acutally more ridiculous than that. Because Tartaglia also didn't want to publish how he did it. He was later convinced by Gerolamo Cordano to explain him his method. Tartaglia did make Cordano swear on everything he would never publish it. When writting his book "Ars Magna" Cordano really wanted to add Tartaglias explanation and his puppil Ludovico Ferrari came to his help. Ferrari had gotten his hands on del Ferro's notes about the equation(he had died before the Tartaglia and Fior Duel and his old notes where sold out by his family) . He gave it to Cordano, who now was no longer bound to the oath to Tartaglia because he could have gotten solution from del Ferro's note. So he published the explaination to the equation in his book quoting Tartaglia and del Ferro as the minds behind that equation. Tartaglia was not amussed and tried to copy strike Cordano and they started the biggest intelectual beef of their time. Ferrari found it super funny and kept teasing Tartaglia until they had a duel. Ferrari mobbed the floor with Tartaglia. Cordano and Ferrari became famous while Tartaglia lost all his honour and reputation.

Sometimes history really ia funnier and better than fiction.