Magic carpets are generally safe. It’s hard to fall and get hurt unless you’re stupid.

If it’s you doing the flight magic, it helps to focus your levitation on an object underneath you, like a carpet, a broom or whatever. It would feel stable like sitting on a pool floatie. If you got yourself up in the air and lose the carpet somehow, you probably have enough flying skill to land safely without one. Now, if you fly 2-3 km up and lose consciousness from lack of oxygen, you’re cooked.

If you aren’t magical and the carpet is doing all the work, then the carpet is your mount, like a horse. Well-trained mounts can feel the rider’s weight shift around and try to keep you seated. Just don’t make the carpet angry, or it might buck you off.