The most important reason for installing a cap, is that it will keep out any/all animals that might want to make a home out of your fireplace flue. Some animals can cause damage to the clay liner when going up and down the flue.
A reason not to install a cap is because the rain/snow will help clean off your flue tiles. Yes it will take that soot and deposit it behind or on top of your damper, but it will help rinse the flue off.
Let us know if we can answer any more questions you might have.
General advice. Contact licensed chimney expert for your particular situation.
For years, people throughout the greater Milwaukee and Waukesha areas have been turning to Smoke Stacks, Inc. for their chimney repair and relining needs. At Smoke Stacks, Inc. we believe that attention to detail, professional work, courteous service and honest prices are the qualities that make the difference.