They could not actually. Special Edition wouldn't even exist. Shortly after the production of Devil May Cry 3: Dante's Awakening they started working on Devil May Cry 4. After a few months they saw that ps2's power is insufficient for Devil May Cry 4. Then they took Dante's awakening and did some edits. They took the hardware from Vergil from when he is a boss and made it playable while altering it a little. They made the arena to fight enemies and bosses using the same program from Devil May Cry 2 with some improvements of course, known as Bloody Palace. They made 2 cut-scenes and some costumes for Vergil along with the Super Sparda for Dante and I think, that's where they thought that's enough and returned to Devil May Cry 4.
The thing is, they could have made the actual game like this and better and start working on Devil May Cry 4. But still it's rather enjoyable and we shouldn't complain