The Batmobile would be cool, as long as it had an option to play Joker's Jingle bells(Jingle bells, Batman smells, Robin laid an egg, the batmobile lost a wheel and the Joker got away!!!).
Although it would be cool, there would be some issues with it. For starters, it would distract from roaming on rooftops, which the game has a large focus on watching from up high. Also, I think there are a lot of obstacles on the roads and criminals, ans since Batman doesn't kill people, it would be hard to drive around. It would also take away from the players view of all the details in the game, like how people abused the Detective mode in AA and it lowered the visual quality.
I think it would be cool to have the Batmobile, but again, I could see issues with it as the game is currently constructed.
Here's the clip from Christmas with the Joker that has the Joker's Jingle Bells:
Mark Hamill is the best Joker in my opinion, Heath is close, but his was much too serious. Hamill's was dark, but his also had that really twisted humor side. Check out the rest of Christmas with the Joker to see Hamill's dark humor. Not that Ledger's Joker was bad, it was great, but his was much more realistic and sociopathic killer like, while Hamill was more well cartoony, I guess. It's hard to explain, but they're different ways to interpret the character.