Because the Punic Wars showed the flaws of elephants are as a weapon once you know how to counter them?

Really elephants are impressive, they can scare a poorly disciplined or unmotivated army like those Carthage was used to fight but that's about it. They are easily startled, in which case they turned back and fled in panic, trampling your own army, which is not a good thing for a war beast. They were also not very mobile and were not really good at flanking (one of the use of the cavalry). All in all their main asset is the intimidation factor and their ability to carry heavy loads.

They are pretty useful as beasts of burden of course but even then are really ill adapted to European landscapes (they suck at passing rocky / mountain grounds and are not well adapted to cold climates) as proven by the passing of the alps of Hannibal where Hannibal lost the majority of his elephants to the cold.

Follow-up question: Would it have been possible logistically? Was the Roman Empire capable of moving a large animal across great distances without it dying in transport?