Because the mint has a budget and the cost of metals impacts that budget. It is not due to considerations about giving the coin any particular intrinsic value.
Your statement and mine are in alignment. Metal content is changed to reduce the cost to make a coin which results in an intrinsic value lower than face value. The reason that the mint changes coin composition is that the existing composition has an intrinsic value higher than face value. The Mint counts the difference between melt and face value as revenue. If a coin is intrinsically worth more than its face value it is a loss to the Mint. So, they change the composition to be less than face value so that coin makes them revenue again.