This is a pretty incomplete understanding of the issue, there are plenty of dams where silting is not an issue at all and will serve their purpose for centuries if properly maintained. There are also dams where silting is a regular problem. A so called 'sediment bypass' is often a feature of these dams, where water is pulled from the base of the dam through a bypass to clear out silting.

It all depends on the natural hydraulic dynamics of the dam - some are better placed than others.