Can a provisional driver get insurance that covers them in any car they use to practice?

No, you can't. When you take out a car insurance policy, you are quoted a value based on the risk associated with the car in question and the driver. Therefore different cars will need re-assessment of the premiums and that is why such a product does not exist for learners. You can have a learner insurance policy on 1 car that you'd like to drive though, whether it belongs to your friend/family or parent.