I don't know, maybe he just thought it would be cooler to have a Batmobile. I mean realistically you can have superspeed or your own car but deep down you still really wanna drive the Batmobile.
Also in fairness Tim's Car would be in Gotham and the stolen Batmobile was in LA where he would only go on weekends at that point in the run so I can see why his own car wasn't there.