Cato realize that the dispute between Carthage and Rome had to be resolved if the nation was going to move forward. Half assed ceasefires just delay the resolutions of problems.
The problem may be that ethnic problems don't ever get resolved. Cato or not, destroying Carthage was hardly a resolution, turned out. Let's see, Hannibal from Carthage defeated Rome -- twice, IIRC -- once with elephants and Alps involved, very showy.
But eventually Rome not just defeated Carthage, but, justifiably annoyed perhaps, also salted the earth after moving out all the citizens (or enslaving the more valuable ones, usually young and/or female) to a point about 20 miles inland. Carthage having been a port city was a lot of the problem. So they moved them away from the port.
Do I really have to tell you what happened in the fullness of time? They moved back, duh. And although the city was now Roman-governed, it also became a power point in the build-up to the end of the Roman Republic, in the fighting that characterized the whole century before all that Julius Caesar stuff started up. So Carthage and Rome continued to fight.
SOMETIMES it lasts a little longer --- the Huns that did so much to make the Roman Empire fall did disappear for a long time as soon as Atilla the Hun died. But the Huns came back, too -- it just took longer, till about 1250 A.D, some 800 years. And then of course they came back again 300 years later, if you count the Turks, and I do, all the way to Vienna --- 1529--1683. If you consider the Huns Chinese, and I do, things aren't looking real good on that front right now. It was the Huns, after all (a Mongol horde) that threw the plague corpses over the walls into the Genoese trading post of Kaffa in 1347 and thus produced the Black Death of 1348 all over Europe. Did they just do that again? One wonders.