Is it common for automated control systems to use non-redundant sensors?
In general, yes. Except in certain configurations, namely autoland, autoflight functions are usually fed with one set of sensors.

This matches the fact that pilots flight instruments are fed from a single source as well. Therefore, the autopilot behavior and instruments should have a coherent and predictable response.

The main reason is fault isolation. If the flight crew identifies a fault with the captain's instruments, then disabling instrumentation and autoflight functions on the captain's side will guarantee the faulty data will not influence the copilot's instrumentation and controls.

If you have the system try to "intelligently" vote, you run the risk of not being able to isolate a faulty sensor, especially in 2 faulty of 3 sensor situations. Another classic problem is how to prevent the voting system from becoming a single point of failure.

Instruments are accompanied by a comparator, which detects significant differences between redundant readings and causes an appropriate warning. Most systems treat the warning as binary: the flight crew manually compares all readings and using human logic, decides which are discrepant.