What makes you think the Allies were actively hunting them? Soviet Tass was the first to report that Hitler fled to Argentina in July 1945, but no one cared to pressure the Argentine government about it. (The Argentines didn't want' to give up a productive ethnic European population, or the plundered wealth the Nazis brought with them.) Only Israelis like Simon Wiesenthal were actively looking for prominent Nazis. They only found Joseph Mengele after he was dead and buried. According to the declassified 1955 CIA report about Hitler's visit to Columbia, the CIA bosses declined to pursue the matter because it would be too expensive, which is to say it was not important, or that they just didn't want to probe the matter further. The CIA didn't want to hunt Hitler.
And what was he going to do if he had escaped? Do you think that he would have settled into a quiet retirement in the Argentine countryside sipping tea and eating cakes and painting pictures? Would the man who made Europe tremble under his boots settle for that? Or would this burned out middle aged shell of a man with multiple serious health issues (possibly including Parkinson’s Disease) want to start all over in a country In which he had no ties?
South America's ethnic German communities experienced fantastic growth after WWII from the escaping Nazis. According to the books that were written about Hitler in Argentina, Hitler and Eva Braun had two daughters there, who were still alive at the turn of the millennium. As the leader of Germany, Hitler didn't want to get married because his family would have been at risk. After the war, that didn't matter. He spent his time enjoying the Andes, as he had the Alps in Europe.
The German community respected him as an elder leader much like prisoners who rebelled and briefly take over a prison respect their leaders. They remember that it was good the short time it lasted.
And what kind of legacy would he have left Germany if he had fled like a coward instead of going down with the Reich? The escape conspiracy buffs never seem to have an answer to those questions.
He made Germany a better place by leaving. The Nazis were always aggressive animals testing the limits in Europe. There was nothing noble about them. The Nazis ran away to South America in the same way a pack of wolves will disperse back into the forest once someone fires a shot at one of them. Churchill said the Germans were either at our throats or at our feet. In South America, they lacked sufficient numbers to threaten anyone and stayed at the feet of the respective governments. The Nazis benefited South America, and in turn South America turned a blind eye to them.