Carry road bike inside an SUV
There is no real problems other than things getting scratched or broken being shuffled around, derailleurs easily get caught on seat belts etc. There is however a very easy and affordable option to avoid this. (Assuming you have QR skewers)

Install a 2x4 or similar piece of wood. Then mount QR truck mounts to said 2x4. If you are going to be using your SUV to carry your bike very often this is the way to go if you don't want to spend the money on a roof or trunk rack. Generally, and depending on SUV make and model you can easily fit more than one bike using this method.