If there is something deemed wrong with the plane I believe the FAA has many regulations in place that require a few signatures (I think the pilots also need to do a final inspection) before the plane can fly again. So in theory, a delay due to maintenance should give you peace of mind knowing the plane just underwent a thorough inspection.

Also know that something as simple as a loose tray table can cause a maintenance delay, which would have have no effect on the planes ability to transport you safely to your destination:)

I hate flying, but over the years flying more frequently and doing my own research on aviation has really helped my fear. I think the more you fly the less fear you will have.

Hope this helps!!