It feels like giving control to a 3rd-party on all your proprietary data. You would feel more comfortable having a physical server, allocating space while setting up the environment for that server, and paying for support when things go south. It even brings peace of mind that comes from knowing that, if all else fails, you can go in and fix the hardware yourself because you think you have full control.
However, it is important to distinguish between “doing the donkey work” and “having control”. If anything, you have more control over what you’re deploying on with cloud platform, since you have no fixed allocation of resources – you use as much or as little as you need and that leads to savings.
By the way, owning your own hardware and keeping your servers within arm’s reach does not necessarily keeps it safe. Without proper management system in place, data can still leak out.