For the same reason that Whitebeard never avenged Oden's death... because a Yonko vs. Yonko fight would probably cost the lives of many of his dear subordinates (sons, in the case of WB).
By pre-timeskip (pre Marineford), Shanks didn't really know where Blackbeard was, and even if he did knew, I don't think he could waste his time looking for a yet-to-be-developed threat... he's a Yonko after all and needs to take care of his own business. Remember that, after following Drum's lead, it took at least a month for Ace to find Blackbeard (I'm counting the days from the start of the Drum Arc to the end of Post-Enies Lobby; it's a little more than a month, but Ace probably started his search even earlier)... imagine how things would become if he were to leave his protected territories in the New World for a month (look at what happened when Big Mom left WCI, she had Pudding kidnapped and probably had her Road Poneglyph stolen). It's totally different from meeting with Whitebeard or the Gorosei, who have known whereabouts (or even permanent residence, in the case of the Gorosei).
By Marineford, Shanks went there to stop the war. If he did start a fight with Blackbeard from the get go, he would've risked his crew and maybe even his own life, specially if the marines kept fighting (which they probably would do). However, the mood was quickly soured and the Red Hair Pirates didn't shy away from Blackbeard's teasing, it was BB who ultimately withdrew.
IMO, I think that the best opportunity was during the timeskip, right after Blackbeard conquered Hachinosu. However, the rumors about Aokiji joining Blackbeard must've caught the attention of Shanks, and he probably deemed a direct confront too risky. That's why he went to Wano to take Blackbeard by surprise, this way BB wouldn't have his full crew and the territorial advantage on his side (despite having the Gura Gura no Mi, which gives a huge advantage to BB in naval warfare, but I guess that Shanks has means to counter or at least overcome that).