In previous editions part of what made the Tarrasque so difficult an opponent was its ability to rise from the dead (even if disintegrated) unless the party used a wish spell to prevent its resurrection (to say nothing of a sadistic DM perverting said wish depending on how the players phrased it), yet the monster's statistics in the 5th Edition Monstrous Manual make no mention of this. Should one assume this is no longer a requirement?
As you mention, the 5e Monster Manual says nothing about needing a wish to permanently kill a Tarrasque.
Since it doesn't say you do, then you don't.
There have been many changes between editions, this is obviously one of them.