Did my home's builder not properly protect the outside molding from water?
Yes there should be flashing but that isn't the main issue.

This is the architect's problem.  The top of your molding is flat.  Where do you think water will go on a flat surface?  It will sit on it.  It will then seep into the wood and to the wood underneath it, slowly water logging and rotting all of it.  If someone showed me your new molding I would imagine this in 3-4 years.   You are lucky for it to last that long.

You need to replace the wood.  Then add flashing but more importantly add a triangular piece to the top that slopes out.  If all of the water slopes off of this at the top and you paint it every 5-8 years you will be fine.